Question

Please help me with a question that involves derivatives! I thought I was doing the problem was correctly, but the answers in the textbook is different

Answer 1

i don't understand what's happening in your third line
you want the derivative of \(x^2\sin x\) at x=3 ?

Answer 2

or is this a linear approximation?

Answer 3

Yeah.

Answer 4

I thought I got the derivative properly.

Answer 5

yes, line 2 is correct
I don't quite understand what you want though, do you want the equation for the tangent line at x=3 or what?

Answer 6

I need to find out the tangent line at x=3.

Answer 7

Can you see where I went wrong? In the previous question I asked, someone said to use the formula y=(derivative of f(a))*(x-a)+(f(a))

Answer 8

In this problem its not working though and I don't know why.

Answer 9

well for one thing you wrote 9cos3 when plugging in x-3 for x^2-cosx should give 9-cos3

Answer 10

x=3*

Answer 11

i think that's the only error

Answer 12

Okay. but why should it be 9-cos3?

Answer 13

oh i misread your writing

Answer 14

what is the answer supposed to be?

Answer 15

cause it looks right but i haven't busted out the calculator

Answer 16

The answer is supposed to be (9cos3 + 6sin3)x - 27cos3 -9sin3

They say the decimal approximation is y=-8.063x+25.460

Answer 17

and how is that not what you have?
your expression simplifies to (9cos3 + 6sin3)x - 27cos3 -9sin3
it must e a calculator error perhaps radian/degree issue

Answer 18

yep checks out in radians just fine

Answer 19

OHHHHH!!!!! Omg it was a silly mistake I was making!! I'm sorry for spending so much time on this problem!!

Answer 20

haha it happens to the best of us. and me

Answer 21

Thanks so much for helping me! I'm sorry!!

Answer 22

no worries! you'll only make that mistake 100 more times before you get past it, just part of the process ;)