Question

Find the critical numbers of f(x)=x3+3x2+3x−6.

Answer 1

x = -1

Explanation:

`f(x)=x^3+3x^2+3x-6\\f'(x)=3x^2+6x+3\\\\0=3x^2+6x+3\\0=x^2+2x+1\\0=(x+1)^2\\0=x+1\\x=-1`

Therefore, the only critical number of f(x) is x=-1