I don't understand the explanation I'm given. Can someone help me for a medal?

Question

anonymous · Answer

I'll post it in just a second

anonymous · Answer

attachment

anonymous · Answer

How did they get from 1. to 2. ? I get a different derivative when I solve it out

jahmiya · Answer

@superman38  do you understand this

anonymous · Answer

uh naq just lookin at it

anonymous · Answer

I just need the first derivative. Everything else, I can probably do on my own.

anonymous · Answer

It obviously provides it, but I'm curious to know how that got that as their answer.

campbell_st · Answer

so do you know what the 2nd derivative test is...?

campbell_st · Answer

ok.. so if 
$$g(x) = 2x^2(1 - x^2)$$

if you distribute it can be written as 

$$g(x) = 2x^2 - 2x^4$$

now take the derivative 

$$g'(x) = 4x - 8x^3$$

so in factoring this 4x has been taken out as the common factor 

$$g'(x) = -4x(-1 + 2x^2)~~~~~or~~~~~~g'(x) = -4x(2x^2 - 1)$$

anonymous · Answer

OH! Factoring! I kept getting 4x - 8x^3  and couldn't figure out what to do next. Thank you. It makes sense now.

anonymous · Answer

(by the way, I wasn't watching my computer, so that's why I didn't respond when you originally posted. sorry about that)