Find and justify the inflection point.

01 / Standard#Your turn

f(x)=x^3-12x+6

Official paper · jm02-2023 · 2(a)(iii) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Set f″=0.

Hint 2

Check the sign change of 6x.

Worked solution

Concavity changes from down to up at zero.
$x<0\implies f''<0,\quad x>0\implies f''>0$
Evaluate the ordinate.
$f(0)=6\implies(0,6)$

Inflection point (0,6).

Checks and common pitfalls: The point need not have a horizontal tangent.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Concavity changes from down to up at zero.
$x<0\implies f''<0,\quad x>0\implies f''>0$
Evaluate the ordinate.
$f(0)=6\implies(0,6)$

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

2023 JM02