critical x^3-27 — step-by-step solution

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

⇥Let's perform the differentiation:

\frac{d}{d x} (x^{3} - 27)

⇥ⓘ The derivative of a sum is the sum of the derivatives:

\frac{d}{d x} (x^{3} - 27)

\frac{d}{d x} (x^{3}) + 0

⇥

\frac{d}{d x} (x^{3}) + 0

⇥ⓘ Adding 0 changes nothing:

\frac{d}{d x} (x^{3}) + 0

\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

is equivalent to:

x = 0

▶Solution obtained:

x = 0