Define for all in the common domain of the two terms.

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

Problem

Define

h(x)=\sec x + \csc x

for all

x

in the common domain of the two terms. (a) Compute

h'(x)

. (b) Determine the exact value of

h'\!\left(\dfrac{\pi}{4}\right)

. Show all work leading to your result. (c) Based on your result in part (b), indicate whether

h

is increasing, decreasing, or neither at

x=\dfrac{\pi}{4}

. Justify your conclusion.