Let be defined on the interval .

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

Problem

Let

h(x)=5\sin(2x)+x

be defined on the interval

[0,2\pi]

. (a) Compute the average rate of change of

h

over

[0,2\pi]

. (b) Solve

h'(x)=m

, where

m

is the average rate from part (a), and list every solution

c

(0,2\pi)

. (c) Determine the total number of such values

c

and explain, using properties of

h'(x)

, why no additional solutions occur in

(0,2\pi)