Given f(x) = cubed root of x^2 (2x+5)^3, find the critical numbers after you identify the domain.

Answer 1

I assume you mean (∛x^2)(2x+5)^3

∛ has domain all reals
all polynomials have domain all reals.

f' = 2(2x+5)^2(11x+5) / 3∛x

Now we see that f' is undefined for x=0
f'=0 for x = -5/2 and -5/11