Let ` a , b in R and f:R to R` be defined by f(x) `=a cos (|x^(3)-x|)+b |x|sin (|x^(3)+x|)` then f is

Options

A. differentiable at x=0, if a=0 and b=1
B. differentiable at x=1, if a=1 and b=0
C. not differentiable at x=0, if a=1 and b=0
D. not differerntiable at x=1, if a=1 and b=1

Answer

A, B

Explanation

We have `f(x)=a cos(|x^(3)-x|)+b|x|sin(|x^(3)+x|)"for all"x in R`
`Rightarrow f(x)=a cos(x^(3)-x)+bx sin(x^(3)+x)"for all "x in R`
Clearly, f(x) is the sum of two continuous and differentiable functions for all `x in R`. Hence options (a) and (b) are correct.