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mathcalculus
 2 years ago
helpppp: find the critical points: s(t)= (t1)^4 (t+5)^3
mathcalculus
 2 years ago
helpppp: find the critical points: s(t)= (t1)^4 (t+5)^3

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calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0@mathcalculus , what have you tried?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yes, i used the product rule: \[\frac{ d }{ dx } (t1)^{4}* (t+5)^{3}= (t1)^{4} * 3(t+5)^{2} + (t+5)^{3} * 4(t1)^{3}\]

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0then from there, i'm stuck.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0ok, so far so good. Now, factor out the greatest common factor of both terms. For example, they both have a factor of (t1)^3, but that's not all they have in common. What else?

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Don't they both have a factor of t+5 to a power?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0oh yes, but are from opposite sides..

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0doesn't matter the order. AB+CA=A(B+C)

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0can you explain to me. i dont really see where we are going with factoring

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0The purpose in factoring is to simplify the derivative into a product of three factors. One of the factors will be t1 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
 2 years ago
Best ResponseYou've already chosen the best response.0And then once you have your derivative in factored form, you can set each factor equal to zero to find your critical points.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i understand what youre saying but not how sure how to do that.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Ok, lets look at the t1 term in each expression.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0What is the largest exponent they share?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0now i know that i write (t1)^3

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0but what happens to the 4?

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Exactly, so, we may factor out a \[\left( t1 \right)^{3}\] from both expressions. Hang on, we will come to that.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Let's take a looke at the first expression in its entirety. If all you are removing is the \[\left( t1 \right)^{3}\] You would be left with \[4\left( t+5 \right)^{3}\]

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0no if i was to see the common factor.. i would get (t1)^3+ (t+5)^2.... then what do i do with the numbers that are left...?

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0ok,, there is your mistake. It isn't a sum. It's a product.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0ok so i dont see how you got 4(t+5)^3

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Hang on, I was only talking about factoring out the t1 from the first expression,, not from the whole thing.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0well you showed me that

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Hang on my pc is giving me fits.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0On 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
 2 years ago
Best ResponseYou've already chosen the best response.0i understand this part... (t1)^3* (t+5)^2

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Rememmber when I was saying if all we factored out was the (t1)^2 You would have the 4(t+5)^3 left.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0but then i dont understand why it is 4(t+5) ... i did this..4(t1) + 3(t+5)

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Well, 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
 2 years ago
Best ResponseYou've already chosen the best response.0im left with 7t+17

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Perfect. 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
 2 years ago
Best ResponseYou've already chosen the best response.0That is one of your critical points. There are two others.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Now you have one more to do.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Tinme for lunch, I will come back shortly to see if you have finished it.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0the exponent is in the way.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Well, raise each side to the 1/3 power. That will get rid of your exponent.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0kkk but how do we find the y

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Just go back in and substitute the critical values.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0For t=1 and t=5, you will get y=0. But for t=17/7, you won't get y=0.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0and 17/7 i got a huge number.. doesn;t make sense.. :(

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Well, 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
 2 years ago
Best ResponseYou've already chosen the best response.0i see that but it keeps saying the critical points are wrong.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0ok, I need to see the original problem. And what keeps saying your critical points are wrong?

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Are you using an online program?

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Your value for t=17/7 is incorrect

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0You should get a large numerator divided by a denominator of 7^7.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so i dont know where i went wrong...

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0The numerator should be (24)^4(18)^3

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0we did this step by step... now t is wrong?? really?

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0No, t is not wrong, but your evaluation of the function for t=17/7 is incorrect.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so now how do i solve that?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0obviously i know its wrong.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0ive tried this problem out 3294810347 times.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Should have (17/71)^4(17/7+5)^3

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0\[\frac{ 17 }{ 7 }1=\frac{ 24 }{ 7 }\] and \[\frac{ 17 }{ 7 }+5=\frac{ 18 }{ 7 }\]

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0wow this is insane. ive spent an hour to 2 with this problem.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0why?? why did we ignore the exponents???

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Now raise each of those terms to the appropriate powers.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0sn;t it suppose to be part of it?? the original problem we were given??

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0we didn't I was just showing you step by step.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0thats how i got the hugeeeeeeee number

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0and so did i. i had it on paper.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0what i dont understand is that youre basically saying raise those to the power.. in other words, im redoing this whole crap again.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Well, the numerator should be larger than your denominator, and it wasn't according to your answer.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0which AGAIN, is leading m to the wrong huge answer i had before

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0No, you are finding the yvalue that goes with the value you ccame out for t.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so there are 4 crtical points now?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0youre saying raise hem to the power and multiple right???

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0do you know rasing them to the power is going to GIVE ME A HUGEEEEEE NUMBER??

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0do you not see that was what i had in the first place??

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0There are only the three values of t we came up with, but you want them as ordered pairs, yo

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0ok good3 values done.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0obviously i want them in order pairs.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i did EXACTLY what you just did with the 17/7 and got those numbers.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0I see that, but your answer for t=17/7 showed a smaller numerator than denominator and it shouldd be the other way around.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0whats the y value for 17/7

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0How did you do that? Each numerator is larger than each denominator and they both have total of 7th powers.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0ok find the answer.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i need to see if it's correct

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i cant keep wasting 23 hours on one problem.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0@calcmat, are you stuck?

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0\[\left( \frac{ 24 }{ 7 } \right)^{4}\times \left( \frac{ 18 }{ 7} \right)\]

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0now 18/7 needs to be raised to the 3rd power.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0ACCORDING TO THE ORIGINAL PROBLEM

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Should gha have a 3 on the second expression for the power.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0and i just proved my point. you are taking em to the wrong direction AGAIN.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0What are you talking about.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0I ASKED YOU ONE SIMPLE QUESTION. CAN YOU FIND THE ANSWER?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0I WANT TO SEE IF WHAT YOU'RE DOING IS ACTUALLY CORRECT

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0IVE SPENT 23 HOURS WITH YOU IN THIS PROBLEM.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Hey, don't get mad at me, I am the one spending MY TIME helping YOU.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0YOURE STILL NOT ANSWERING MY QUESTION.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0You can answer the question by taking (24/7)^4(18/7)^3

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0I DID. STILL A HUGE NUMBER

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0I got 2349.5 rounded to 1 decimal place.

dan815
 2 years ago
Best ResponseYou've already chosen the best response.0(1+t)^3 (5+t)^2 (17+7 t) your 0's = 1,5,17/7

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0nvm. i''ll solve it

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Those are the ones I got @dan815

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0that part is correct.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0and @calmat01 don't round. thats wrong.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0keep the numbers just the way they are. p.s found the answer. thanks.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Ok, so my answer wasn't completely off?

dan815
 2 years ago
Best ResponseYou've already chosen the best response.0mathcalculus can you prove the divergence theorem for me?

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0So you are telling me that you should have left the answer as 1934917632/823543? That's insane @mathcalculus

dan815
 2 years ago
Best ResponseYou've already chosen the best response.0what are all these big numbers?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0your explanation was confusing. but the numbers are correct.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Gee, I spent all that time being patient with you, and all I get is my explanation was confusing?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0lol truth to be told...truth be told.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0I 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
 2 years ago
Best ResponseYou've already chosen the best response.0I 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.
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