Mathematics

Problem

Consider the function

h(x)=\sin x- x\cos x

defined on the interval

0< x <2\pi

. a. (i) Show that

h'(x)=x\sin x

and hence find all values of

x

(0,2\pi)

for which

h'(x)=0

. b. (ii) Obtain an expression for

h''(x)

. c. (iii) For each stationary point found in part (i), decide whether it is a point of local maximum or local minimum. Write the corresponding ordered pairs

(x,h(x))

using exact values. d. (iv) State which, if any, of these stationary points gives the greatest value of

h

(0,2\pi)

Browse the problem library