Find the inflection point and verify the concavity change.

01 / Standard#Your turn

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

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

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Solve 6x+6=0.

Hint 2

Substitute the resulting x into f.

Worked solution

Inflection point (−1,−2).

Checks and common pitfalls: An inflection concerns concavity, not necessarily a stationary point.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The second derivative changes from negative to positive at −1.
$f''(x)=6(x+1)$
Evaluate its ordinate.
$f(-1)=-1+3-4=-2$

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

2025 JM02