Question

If f(x)=2ax^3+x^2 and f'(x)=0 what is a?

Answer 1

`x=-(1)/(3a)`

Explanation:

`f(x)=2ax^3 +x^2 \implies f'(x)=6ax^2 + 2x \\ \\ \therefore 6ax^2 + 2x=0 \\ \\ 2x(3ax+1)=0`

Since f'(x)=0 for all x, we can ignore the case x=0.

`3ax+1=0 \\ \\ 3ax=-1 \\ \\ x=-(1)/(3a)`