Find the first and second derivatives.

01 / Standard#Your turn

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

Official paper · jm02-2026 · 2(a)(i) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Differentiate each power term.

Hint 2

Differentiate the first derivative once more.

Worked solution

f′=3x²−2x−1; f″=6x−2.

Checks and common pitfalls: The derivative of −x is −1.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Differentiate the cubic.
$f'(x)=3x^2-2x-1$
Differentiate the quadratic derivative.
$f''(x)=6x-2$

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

2026 JM02