Mathematical Methods — Question 3

QCAA 2022, Paper 2 · 1 mark

Q3 · 2022 · Technology-activeSimple familiar1 mark

QUESTION 3

The derivative of the function

f(x)

is given by

f'(x)=\sin(x^3)

for the domain

-1.8<x<1.8

. The number of points of inflection that the graph of

f(x)

has on this interval is

(A)

1

(B)

3

(C)

4

(D)

5

ABCD

WORKED SOLUTION

1 mark

ANSWER

C —

4

Worked solution

f''(x)=3x^2\cos(x^3)

. Inflection points occur where the concavity changes; counting the zeros of

\cos(x^3)

that produce sign changes in the stated interval gives 4. Therefore C.

Selects option C.

[1 mark]

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