Find the first two derivatives.

01 / Standard#Your turn

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

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

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Differentiate each polynomial term.

Hint 2

Differentiate once more.

Worked solution

f′=3x²−12, f″=6x.

Checks and common pitfalls: The original constant 6 disappears on differentiation.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Apply the power rule.
$f'(x)=3x^2-12$
The derivative of the constant −12 is zero.
$f''(x)=6x$

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

2023 JM02