helpppp: find the critical points: s(t)= (t-1)^4 (t+5)^3

- anonymous

helpppp: find the critical points: s(t)= (t-1)^4 (t+5)^3

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- anonymous

@mathcalculus , what have you tried?

- anonymous

yes, i used the product rule:
\[\frac{ d }{ dx } (t-1)^{4}* (t+5)^{3}= (t-1)^{4} * 3(t+5)^{2} + (t+5)^{3} * 4(t-1)^{3}\]

- anonymous

then from there, i'm stuck.

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## More answers

- anonymous

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?

- anonymous

?

- anonymous

Don't they both have a factor of t+5 to a power?

- anonymous

oh yes, but are from opposite sides..

- anonymous

doesn't matter the order. AB+CA=A(B+C)

- anonymous

can you explain to me. i dont really see where we are going with factoring

- anonymous

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.

- anonymous

And then once you have your derivative in factored form, you can set each factor equal to zero to find your critical points.

- anonymous

can you show me

- anonymous

i understand what youre saying but not how sure how to do that.

- anonymous

Ok, lets look at the t-1 term in each expression.

- anonymous

ok

- anonymous

What is the largest exponent they share?

- anonymous

3

- anonymous

now i know that i write (t-1)^3

- anonymous

but what happens to the 4?

- anonymous

Exactly, so, we may factor out a \[\left( t-1 \right)^{3}\] from both expressions. Hang on, we will come to that.

- anonymous

k

- anonymous

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 \[4\left( t+5 \right)^{3}\]

- anonymous

Do you see that?

- anonymous

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...?

- anonymous

ok,, there is your mistake. It isn't a sum. It's a product.

- anonymous

ok so i dont see how you got 4(t+5)^3

- anonymous

Hang on, I was only talking about factoring out the t-1 from the first expression,, not from the whole thing.

- anonymous

well you showed me that

- anonymous

Hang on my pc is giving me fits.

- anonymous

kk

- anonymous

|dw:1363286087022:dw|

- anonymous

why 4(t+5)?????

- anonymous

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.

- anonymous

i understand this part... (t-1)^3* (t+5)^2

- anonymous

Rememmber when I was saying if all we factored out was the (t-1)^2 You would have the 4(t+5)^3 left.

- anonymous

but then i dont understand why it is 4(t+5) ... i did this..4(t-1) + 3(t+5)

- anonymous

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).

- anonymous

okkk

- anonymous

i understand...

- anonymous

im left with 7t+17

- anonymous

t= -17/7

- anonymous

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.

- anonymous

That is one of your critical points. There are two others.

- anonymous

ok so (t-1)^3 = 0

- anonymous

Good.

- anonymous

x= 0?

- anonymous

Not quite.

- anonymous

If (t-1)^3=0 then t=1

- anonymous

Now you have one more to do.

- anonymous

1? how?

- anonymous

Tinme for lunch, I will come back shortly to see if you have finished it.

- anonymous

the exponent is in the way.

- anonymous

Well, raise each side to the 1/3 power. That will get rid of your exponent.

- anonymous

brb

- anonymous

kkk but how do we find the y

- anonymous

Just go back in and substitute the critical values.

- anonymous

For t=1 and t=-5, you will get y=0. But for t=-17/7, you won't get y=0.

- anonymous

i did....

- anonymous

(1-1)^4 (1+5)^3

- anonymous

=0

- anonymous

and -17/7 i got a huge number.. doesn;t make sense.. :(

- anonymous

i got -432/823543

- anonymous

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!

- anonymous

??

- anonymous

i see that but it keeps saying the critical points are wrong.

- anonymous

=(

- anonymous

ok, I need to see the original problem. And what keeps saying your critical points are wrong?

- anonymous

Are you using an online program?

- anonymous

webwork.

- anonymous

yes

- anonymous

hang on.

- anonymous

##### 1 Attachment

- anonymous

i attached it.

- anonymous

Your value for t=-17/7 is incorrect

- anonymous

why?

- anonymous

You should get a large numerator divided by a denominator of 7^7.

- anonymous

so i dont know where i went wrong...

- anonymous

The numerator should be (-24)^4(18)^3

- anonymous

we did this step by step... now t is wrong?? really?

- anonymous

No, t is not wrong, but your evaluation of the function for t=-17/7 is incorrect.

- anonymous

so now how do i solve that?

- anonymous

obviously i know its wrong.

- anonymous

ive tried this problem out 3294810347 times.

- anonymous

now what do i do?

- anonymous

Should have (-17/7-1)^4(-17/7+5)^3

- anonymous

huhhh???

- anonymous

\[-\frac{ 17 }{ 7 }-1=-\frac{ 24 }{ 7 }\] and
\[-\frac{ 17 }{ 7 }+5=\frac{ 18 }{ 7 }\]

- anonymous

wow this is insane. ive spent an hour to 2 with this problem.

- anonymous

why?? why did we ignore the exponents???

- anonymous

Now raise each of those terms to the appropriate powers.

- anonymous

sn;t it suppose to be part of it?? the original problem we were given??

- anonymous

i did

- anonymous

we didn't I was just showing you step by step.

- anonymous

thats how i got the hugeeeeeeee number

- anonymous

and so did i. i had it on paper.

- anonymous

what i dont understand is that youre basically saying raise those to the power.. in other words, im redoing this whole crap again.

- anonymous

Well, the numerator should be larger than your denominator, and it wasn't according to your answer.

- anonymous

which AGAIN, is leading m to the wrong huge answer i had before

- anonymous

No, you are finding the y-value that goes with the value you ccame out for t.

- anonymous

so there are 4 crtical points now?

- anonymous

or 3??

- anonymous

youre saying raise hem to the power and multiple right???

- anonymous

do you know rasing them to the power is going to GIVE ME A HUGEEEEEE NUMBER??

- anonymous

do you not see that was what i had in the first place??

- anonymous

There are only the three values of t we came up with, but you want them as ordered pairs, yo

- anonymous

ok good3 values done.

- anonymous

obviously i want them in order pairs.

- anonymous

i did EXACTLY what you just did with the -17/7 and got those numbers.

- anonymous

I see that, but your answer for t=-17/7 showed a smaller numerator than denominator and it shouldd be the other way around.

- anonymous

then show me.

- anonymous

whats the y value for -17/7

- anonymous

How did you do that? Each numerator is larger than each denominator and they both have total of 7th powers.

- anonymous

ok find the answer.

- anonymous

i need to see if it's correct

- anonymous

i cant keep wasting 2-3 hours on one problem.

- anonymous

@calcmat, are you stuck?

- anonymous

\[\left(- \frac{ 24 }{ 7 } \right)^{4}\times \left( \frac{ 18 }{ 7} \right)\]

- anonymous

yeah

- anonymous

now 18/7 needs to be raised to the 3rd power.

- anonymous

ACCORDING TO THE ORIGINAL PROBLEM

- anonymous

Should gha have a 3 on the second expression for the power.

- anonymous

and i just proved my point. you are taking em to the wrong direction AGAIN.

- anonymous

Correct.

- anonymous

What are you talking about.

- anonymous

I ASKED YOU ONE SIMPLE QUESTION. CAN YOU FIND THE ANSWER?

- anonymous

I WANT TO SEE IF WHAT YOU'RE DOING IS ACTUALLY CORRECT

- anonymous

IVE SPENT 2-3 HOURS WITH YOU IN THIS PROBLEM.

- anonymous

Hey, don't get mad at me, I am the one spending MY TIME helping YOU.

- anonymous

YOURE STILL NOT ANSWERING MY QUESTION.

- anonymous

You can answer the question by taking (-24/7)^4(18/7)^3

- anonymous

I DID. STILL A HUGE NUMBER

- anonymous

I got 2349.5 rounded to 1 decimal place.

- anonymous

WRONG BUDDY.

- dan815

(-1+t)^3 (5+t)^2 (17+7 t)
your 0's = 1,-5,-17/7

- anonymous

nvm. i''ll solve it

- anonymous

thanks everyone.

- anonymous

Those are the ones I got @dan815

- anonymous

that part is correct.

- anonymous

and @calmat01 don't round. thats wrong.

- anonymous

keep the numbers just the way they are. p.s found the answer. thanks.

- anonymous

Ok, so my answer wasn't completely off?

- dan815

mathcalculus can you prove the divergence theorem for me?

- anonymous

So you are telling me that you should have left the answer as 1934917632/823543? That's insane @mathcalculus

- dan815

what are all these big numbers?

- anonymous

yes.

- anonymous

lol insane.

- anonymous

your explanation was confusing. but the numbers are correct.

- anonymous

Gee, I spent all that time being patient with you, and all I get is my explanation was confusing?

- anonymous

lol truth to be told...truth be told.

- anonymous

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.

- anonymous

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.

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