critical f(x)=x^3 — step-by-step solution

A polynomial is differentiable on ℝ: its critical points are the zeros of its derivative

⇥Let's differentiate:

\frac{d}{d x} (x^{3})

⇥ⓘ The derivative of x^n is n*x^(n-1):

\frac{d}{d x} (x^{3})

3 x^{2}

⇥

3 x^{2}

⇥Let's solve in

ℝ

3 x^{2} = 0

⇥We simplify the expression by

3

⇥⇥Let's solve in

ℝ

x^{2} = 0

⇥⇥

x^{2} = 0

means that:

x = 0

▶Solution found:

x = 0