Find and justify the inflection point.

01 / Standard#Your turn

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

Official paper · jm02-2022 · 2(a)(iv) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Set 6x−6=0.

Hint 2

Verify a change in sign, then calculate f.

Worked solution

Inflection point (1,0).

Checks and common pitfalls: The concavity check distinguishes an inflection from a mere zero of f″.

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 x=1.
$f''(x)=6(x-1)$
The given zero supplies its ordinate.
$f(1)=0\implies(1,0)$

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

2022 JM02