Question

Find the critical numbers of the function
g(x) = x7 − 7x5
I think its 0,5, and -5. Is that right? help?

Answer 1

Find derivative and factor it....

Answer 2

its 7x^6-35x^4 = 7x^4(x^2-5) or 7x^4(x+5)(x-5) but my online homework says that wrong. Wouldn't it then be 0, 5 and -5 though?

Answer 3

Hmmm, well \((x^2-5) \neq (x-5)(x+5)\)

Answer 4

Think of it as \[
x^2-(\sqrt 5)^2
\]

Answer 5

i thought that was the difference of two squares

Answer 6

But \(5\) is not squared.

Answer 7

I'm not really sure what to do with radical 5 squared. That would just cancel out and it would be x^2-5..

Answer 8

look at my hint

Answer 9

Is it 0, and +-rad5?

Answer 10

yeah

Answer 11

Awesome, Thanks!!