Let on the interval .

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

f(x)= \sin x - \dfrac{x}{2}

on the interval

0\le x\le 2\pi

. (i) Find

f'(x)

. (ii) Determine all points in the interval where

f'(x)=0

. (iii) Divide the interval

0\le x\le 2\pi

into sub–intervals separated by these points and identify on each sub–interval whether

f(x)

is increasing or decreasing. (iv) List the coordinates of all points on the curve where the tangent is parallel to the

x

–axis.