Find the first two derivatives.

01 / Standard#Your turn

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

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

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Differentiate term by term.

Hint 2

Differentiate the result again.

Worked solution

f′=3x²−6x; f″=6x−6.

Checks and common pitfalls: The constant 2 contributes zero to the derivative.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
First derivative.
$f'(x)=3x^2-6x$
Second derivative.
$f''(x)=6x-6$

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

2022 JM02