Question

Find any critical numbers of the function f(x)=x^2(x^2−64).

Answer 1

Find f'
Set f'=0

Answer 2

Solve f'=0 for x :)

Answer 3

Dont you have to set the derivative equal to 0?

Answer 4

Yep.

Answer 5

I am confused on what the derivative is of this

Answer 6

You know product rule you have a function times another function.
You have x^2 times (x^2-64)

Answer 7

\[(fg)'=f'g+fg' \]

Answer 8

okay thats what i thought

Answer 9

Then the two numbers that make that 0 are 0 and 8 i thought

Answer 10

You need to find [x^2(x^2-64)]'

Answer 11

You need to use the product rule....
Or!
You could distribute x^2 first then just use power rule for both terms.

Answer 12

Okay after I have the derivative of that, what is the next step

Answer 13

2x(x^2-64)+x^2(2x)

Answer 14

?

Answer 15

Right! :)
Now set that equal to 0 and solve for x.