mathcalculus
helpppp: find the critical points: s(t)= (t-1)^4 (t+5)^3
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calmat01
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@mathcalculus , what have you tried?
mathcalculus
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yes, i used the product rule:
\[\frac{ d }{ dx } (t-1)^{4}* (t+5)^{3}= (t-1)^{4} * 3(t+5)^{2} + (t+5)^{3} * 4(t-1)^{3}\]
mathcalculus
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then from there, i'm stuck.
calmat01
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ok, so far so good. Now, factor out the greatest common factor of both terms. For example, they both have a factor of (t-1)^3, but that's not all they have in common. What else?
mathcalculus
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?
calmat01
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Don't they both have a factor of t+5 to a power?
mathcalculus
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oh yes, but are from opposite sides..
calmat01
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doesn't matter the order. AB+CA=A(B+C)
mathcalculus
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can you explain to me. i dont really see where we are going with factoring
calmat01
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The purpose in factoring is to simplify the derivative into a product of three factors. One of the factors will be t-1 to a power, a second factor will be t+5 to a power, and then you will be left with some factor containing a t as well.
calmat01
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And then once you have your derivative in factored form, you can set each factor equal to zero to find your critical points.
mathcalculus
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can you show me
mathcalculus
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i understand what youre saying but not how sure how to do that.
calmat01
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Ok, lets look at the t-1 term in each expression.
mathcalculus
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ok
calmat01
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What is the largest exponent they share?
mathcalculus
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3
mathcalculus
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now i know that i write (t-1)^3
mathcalculus
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but what happens to the 4?
calmat01
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Exactly, so, we may factor out a \[\left( t-1 \right)^{3}\] from both expressions. Hang on, we will come to that.
mathcalculus
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k
calmat01
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Let's take a looke at the first expression in its entirety. If all you are removing is the \[\left( t-1 \right)^{3}\]
You would be left with \[4\left( t+5 \right)^{3}\]
calmat01
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Do you see that?
mathcalculus
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no if i was to see the common factor.. i would get (t-1)^3+ (t+5)^2.... then what do i do with the numbers that are left...?
calmat01
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ok,, there is your mistake. It isn't a sum. It's a product.
mathcalculus
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ok so i dont see how you got 4(t+5)^3
calmat01
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Hang on, I was only talking about factoring out the t-1 from the first expression,, not from the whole thing.
mathcalculus
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well you showed me that
calmat01
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Hang on my pc is giving me fits.
mathcalculus
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kk
calmat01
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|dw:1363286087022:dw|
mathcalculus
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why 4(t+5)?????
calmat01
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On the outside is what they both have in common, on ther inside is what is left after you have factored out that common factor.
mathcalculus
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i understand this part... (t-1)^3* (t+5)^2
calmat01
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Rememmber when I was saying if all we factored out was the (t-1)^2 You would have the 4(t+5)^3 left.
mathcalculus
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but then i dont understand why it is 4(t+5) ... i did this..4(t-1) + 3(t+5)
calmat01
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Well, now we include a (t+5)^2 as well, so what is left from the 4(t+5)^3? Just the 4(t+5).
mathcalculus
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okkk
mathcalculus
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i understand...
mathcalculus
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im left with 7t+17
mathcalculus
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t= -17/7
calmat01
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Perfect. So, now that each expression of the derivative is writtern in factored form, we set each of them equal to zero to find your critical points.
calmat01
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That is one of your critical points. There are two others.
mathcalculus
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ok so (t-1)^3 = 0
calmat01
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Good.
mathcalculus
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x= 0?
calmat01
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Not quite.
calmat01
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If (t-1)^3=0 then t=1
calmat01
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Now you have one more to do.
mathcalculus
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1? how?
calmat01
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Tinme for lunch, I will come back shortly to see if you have finished it.
mathcalculus
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the exponent is in the way.
calmat01
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Well, raise each side to the 1/3 power. That will get rid of your exponent.
calmat01
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brb
mathcalculus
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kkk but how do we find the y
calmat01
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Just go back in and substitute the critical values.
calmat01
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For t=1 and t=-5, you will get y=0. But for t=-17/7, you won't get y=0.
mathcalculus
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i did....
mathcalculus
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(1-1)^4 (1+5)^3
mathcalculus
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=0
mathcalculus
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and -17/7 i got a huge number.. doesn;t make sense.. :(
mathcalculus
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i got -432/823543
calmat01
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Well, you will need to raise some fractions with a denominator of 7 to the 4th and 3rd powers, so yeah, it will get rather ugly!
mathcalculus
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??
mathcalculus
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i see that but it keeps saying the critical points are wrong.
mathcalculus
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=(
calmat01
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ok, I need to see the original problem. And what keeps saying your critical points are wrong?
calmat01
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Are you using an online program?
mathcalculus
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webwork.
mathcalculus
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yes
calmat01
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hang on.
mathcalculus
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mathcalculus
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i attached it.
calmat01
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Your value for t=-17/7 is incorrect
mathcalculus
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why?
calmat01
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You should get a large numerator divided by a denominator of 7^7.
mathcalculus
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so i dont know where i went wrong...
calmat01
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The numerator should be (-24)^4(18)^3
mathcalculus
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we did this step by step... now t is wrong?? really?
calmat01
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No, t is not wrong, but your evaluation of the function for t=-17/7 is incorrect.
mathcalculus
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so now how do i solve that?
mathcalculus
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obviously i know its wrong.
mathcalculus
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ive tried this problem out 3294810347 times.
mathcalculus
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now what do i do?
calmat01
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Should have (-17/7-1)^4(-17/7+5)^3
mathcalculus
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huhhh???
calmat01
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\[-\frac{ 17 }{ 7 }-1=-\frac{ 24 }{ 7 }\] and
\[-\frac{ 17 }{ 7 }+5=\frac{ 18 }{ 7 }\]
mathcalculus
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wow this is insane. ive spent an hour to 2 with this problem.
mathcalculus
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why?? why did we ignore the exponents???
calmat01
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Now raise each of those terms to the appropriate powers.
mathcalculus
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sn;t it suppose to be part of it?? the original problem we were given??
mathcalculus
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i did
calmat01
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we didn't I was just showing you step by step.
mathcalculus
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thats how i got the hugeeeeeeee number
mathcalculus
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and so did i. i had it on paper.
mathcalculus
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what i dont understand is that youre basically saying raise those to the power.. in other words, im redoing this whole crap again.
calmat01
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Well, the numerator should be larger than your denominator, and it wasn't according to your answer.
mathcalculus
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which AGAIN, is leading m to the wrong huge answer i had before
calmat01
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No, you are finding the y-value that goes with the value you ccame out for t.
mathcalculus
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so there are 4 crtical points now?
mathcalculus
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or 3??
mathcalculus
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youre saying raise hem to the power and multiple right???
mathcalculus
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do you know rasing them to the power is going to GIVE ME A HUGEEEEEE NUMBER??
mathcalculus
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do you not see that was what i had in the first place??
calmat01
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There are only the three values of t we came up with, but you want them as ordered pairs, yo
mathcalculus
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ok good3 values done.
mathcalculus
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obviously i want them in order pairs.
mathcalculus
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i did EXACTLY what you just did with the -17/7 and got those numbers.
calmat01
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I see that, but your answer for t=-17/7 showed a smaller numerator than denominator and it shouldd be the other way around.
mathcalculus
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then show me.
mathcalculus
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whats the y value for -17/7
calmat01
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How did you do that? Each numerator is larger than each denominator and they both have total of 7th powers.
mathcalculus
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ok find the answer.
mathcalculus
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i need to see if it's correct
mathcalculus
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i cant keep wasting 2-3 hours on one problem.
mathcalculus
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@calcmat, are you stuck?
calmat01
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\[\left(- \frac{ 24 }{ 7 } \right)^{4}\times \left( \frac{ 18 }{ 7} \right)\]
calmat01
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yeah
mathcalculus
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now 18/7 needs to be raised to the 3rd power.
mathcalculus
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ACCORDING TO THE ORIGINAL PROBLEM
calmat01
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Should gha have a 3 on the second expression for the power.
mathcalculus
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and i just proved my point. you are taking em to the wrong direction AGAIN.
calmat01
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Correct.
calmat01
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What are you talking about.
mathcalculus
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I ASKED YOU ONE SIMPLE QUESTION. CAN YOU FIND THE ANSWER?
mathcalculus
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I WANT TO SEE IF WHAT YOU'RE DOING IS ACTUALLY CORRECT
mathcalculus
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IVE SPENT 2-3 HOURS WITH YOU IN THIS PROBLEM.
calmat01
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Hey, don't get mad at me, I am the one spending MY TIME helping YOU.
mathcalculus
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YOURE STILL NOT ANSWERING MY QUESTION.
calmat01
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You can answer the question by taking (-24/7)^4(18/7)^3
mathcalculus
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I DID. STILL A HUGE NUMBER
calmat01
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I got 2349.5 rounded to 1 decimal place.
mathcalculus
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WRONG BUDDY.
dan815
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(-1+t)^3 (5+t)^2 (17+7 t)
your 0's = 1,-5,-17/7
mathcalculus
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nvm. i''ll solve it
mathcalculus
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thanks everyone.
calmat01
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Those are the ones I got @dan815
mathcalculus
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that part is correct.
mathcalculus
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and @calmat01 don't round. thats wrong.
mathcalculus
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keep the numbers just the way they are. p.s found the answer. thanks.
calmat01
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Ok, so my answer wasn't completely off?
dan815
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mathcalculus can you prove the divergence theorem for me?
calmat01
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So you are telling me that you should have left the answer as 1934917632/823543? That's insane @mathcalculus
dan815
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what are all these big numbers?
mathcalculus
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yes.
mathcalculus
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lol insane.
mathcalculus
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your explanation was confusing. but the numbers are correct.
calmat01
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Gee, I spent all that time being patient with you, and all I get is my explanation was confusing?
mathcalculus
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lol truth to be told...truth be told.
calmat01
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I see. Well, if truth be told, the reason it was confusing was because you forgot how to factor. But I am not bitter. Take care and good luck with the rest of your assignment.
mathcalculus
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I did factor. I just didn't put it up because I was trying to understand you. And also, you were throwing out numbers without reason. & I'm glad you're not so bitter to take my words sensibly:) Thank you.