Find the maximum and minimum of g(x)=f(3sin x).

01 / Standard#Your turn

f(t)=(t-2)^2-9

Official paper · jm01-2022 · II.1(c) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

The inner value t=3sin x ranges over [−3,3].

Hint 2

Compare the vertex and both endpoints.

Worked solution

Maximum 16; minimum −9.

Checks and common pitfalls: Optimise f over the inner range, not over all real t.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The vertex t=2 belongs to the inner range.
$g_{\min}=f(2)=-9$
The farthest endpoint from 2 is −3.
$g_{\max}=f(-3)=25-9=16$

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

2022 JM01