For a fixed real number with

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

For a fixed real number

k

with

|k|<1

, define the function

F(x)=\arcsin(kx)+\arccos(kx)

with domain

|kx|\le 1

. (a) Show that

F'(x)=0

for every

x

in the domain. (b) Compute

F(0)

and thus determine the constant value taken by

F(x)

for all admissible

x

. Explain your reasoning clearly.