Mathematical Methods — Question 1

QCAA 2022, Paper 1 · 1 mark

Q1 · 2022 · Technology-freeSimple familiar1 mark

QUESTION 1

Consider the graph of

f'(x)

for

a\le x\le b

. Which statement describes all the local maxima and minima of the graph of

f(x)

over

a\le x\le b

(A)

one local minimum and one local maximum

(B)

one local minimum and two local maxima

(C)

one local minimum only

(D)

one local maximum only

ABCD

WORKED SOLUTION

1 mark

ANSWER

A — one local minimum and one local maximum

Worked solution

Local extrema of

f

occur where

f'

changes sign. The displayed graph of

f'

crosses the

x

-axis twice: once from positive to negative (a local maximum of

f

) and once from negative to positive (a local minimum of

f

). Therefore A.

Selects option A.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.