Mathematical Methods — Question 5

QCAA 2021, Paper 1 · 1 mark

Q5 · 2021 · Technology-freeSimple familiar1 mark

QUESTION 5

The graph of

f''(x)

is shown. Which of the following could be the graph of

f'(x)

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

The shown

f''

is positive for

x<-1

and

x>1

, and negative for

-1<x<1

. Hence

f'

increases, then decreases, then increases, giving a local maximum near

x=-1

and a local minimum near

x=1

. Only option D has this behaviour.

Selects option D.

[1 mark]

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