Question

Help me simplify this down some more so I can set it to zero and find my critical points.

f(x) = x^3 (x+2)^6

f'(x) = x^3 * 6(x+2)^5 + 3x^2 * (x+2)^6

Answer 1

I see a common factor of 3x^2(x+2)^5

so
x^3 * 6(x+2)^5 + 3x^2 * (x+2)^6

= 3x^2(x+2)^5[2x + x+2}
= 3x^2(x+2)^5(3x+2)

Answer 2

Thanks.