Question

Find the values of x that give relative extrema for the function f(x) = (x+2)^2(x-2).

Answer 1

I think I have to find the derivative first. But I don't know how to do that.

Answer 2

You will need to use the product rule.
(First function)(Derivative of the second function) + (Derivative of first function)(Second function)

Answer 3

F'(x) = (x+1)^2(1)+(2x+2)(x-2)
Like this?

Answer 4

You won't need the product rule if you expand the function.

Answer 5

Ah, true @steve816

Answer 6

Ok. Ill expand right now.

Answer 7

x^3-3x-2
?

Answer 8

Your answer is correct @NY,NY except that the second term should be 2(x+2)(x-2)

Answer 9

*of your previous answer

Answer 10

\[(x+2)^2(x-2)=(x^2+4x+4)(x-2)\]

Answer 11

\[=x^3+4x^2+4x-2x^2-8x-8\]

Answer 12

\[=x^3+2x^2-6x-8\]

Answer 13

Does that look right, or did I make a mistake?

Answer 14

*By the way, both these methods should give you the same answer.

Answer 15

Oh i was so confused but I just realized i typed the question wrong
F(x) is (x+1)^2(x-2)
So sorry about that.

Answer 16

Ah, okay.

Answer 17

Okay, I got what you got

Answer 18

The nice thing about this is that you can take the derivative of each of the terms individually.

Answer 19

Yes
You mean with x^3-3x-2 right?

Answer 20

Because we would take the derivative idividually now
To become 3x^2-3
And x = 1, -1

Answer 21

Absolutely. :)

Answer 22

Thank you.

Answer 23

No worries. Good luck.