Find and classify the local extrema.

01 / Standard#Your turn

f(x)=x^3+3x^2-4

Official paper · jm02-2025 · 2(a)(iii) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Factor f′(x).

Hint 2

Read the sign changes at −2 and 0.

Worked solution

Solve the stationary equation.
$f'(x)=3x(x+2)=0\iff x=-2,0$
The derivative signs are +,−,+. Evaluate f at the critical points.
$f(-2)=0\text{ (local maximum)},\quad f(0)=-4\text{ (local minimum)}$

Local maximum 0 at x=−2; local minimum −4 at x=0.

Checks and common pitfalls: The double zero at −2 touches the axis at a local maximum.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Solve the stationary equation.
$f'(x)=3x(x+2)=0\iff x=-2,0$
The derivative signs are +,−,+. Evaluate f at the critical points.
$f(-2)=0\text{ (local maximum)},\quad f(0)=-4\text{ (local minimum)}$

Think first. Reveal a hint when the class is ready.

2025 JM02