Find the critical numbers

Question

Find the critical numbers of the function f(x)=-6x^5+15x^4+20x^3-8 and classify them using a graph

x= _is a

x= _is a

x=_ is a

Answer 1

Differentiate f(x) and set f'(x)=0.

The roots of f'(x) are 0 of multiplicity 2 and a complex conjugate pair.

This function has a point of inflection with an horizontal tangent at x=0 and no other critical points.