Mathematical Methods — Question 10

QCAA 2020, Paper 2 · 1 mark

Q10 · 2020 · Technology-activeSimple familiar1 mark

QUESTION 10

The approximate value of

x

where the graph of the function

y=x^3+6x^2+7x-2\cos(x)

changes concavity is

(A)

-3.26

(B)

-2.85

(C)

-2.20

(D)

-1.89

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

A change of concavity occurs where

y''=0

. Here

y''=6x+12+2\cos x

. Solving numerically gives

x\approx-1.89

, so D.

Selects option D.

[1 mark]

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