Find the first and second derivatives of f.

01 / Standard#Your turn

f(x)=2x^3-9x^2+12x-5

Official paper · jm02-2021 · 2(a)(i) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Differentiate each polynomial term.

Hint 2

Differentiate the first derivative once more.

Worked solution

f′(x)=6x²−18x+12; f″(x)=12x−18.

Checks and common pitfalls: Do not retain the constant −5 in f′.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Use the power rule.
$f'(x)=6x^2-18x+12$
Constants vanish when differentiated.
$f''(x)=12x-18$

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

2021 JM02