Differentiation of trigonometric functions and differentiation rules — Question 108

Original QCE Vault practice · 1 mark

Q108 · Practice questionTechnology-freeComplex familiar1 mark

QUESTION 108

For

f(x)=x+2\cos x

0<x<\pi

, the stationary points occur at

(A)

x=\dfrac{\pi}{6}

only

(B)

x=\dfrac{5\pi}{6}

only

(C)

x=\dfrac{\pi}{6},\ \dfrac{5\pi}{6}

(D)

x=\dfrac{\pi}{3},\ \dfrac{2\pi}{3}

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

f'(x)=1-2\sin x

. Setting this equal to zero gives

\sin x=1/2

, so

x=\pi/6

5\pi/6

on the interval.

Selects the correct option.

[1 mark]

Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.