Number of points where function `f(x)` defined as `f:[0,2]pivecR ,f(x)={3-|cos x-1/(sqrt(2))|,|sinx<1/(sqrt(2))|2+|cos x+1/(sqrt(2))|,|s in x|geq1/(sqrt(2))` is non-differentiable is a. 2 b. 4 c. 6 d. 0

Options

A. 2
B. 4
C. 6
D. 0

Answer

B

Explanation

`f(x)={{:(3-|cosx-(1)/(sqrt2)|",",|sinx|lt(1)/(sqrt2)),(2+|cosx+(1)/(sqrt2)|",",|sinx|ge(1)/(sqrt2)):}`
`" "={{:(3-|cosx-(1)/(sqrt2)|",",|sinx|gt(1)/(sqrt2)),(2+|cosx+(1)/(sqrt2)|",",|cosx|le(1)/(sqrt2)):}`
`" "={{:(3-cosx-(1)/(sqrt2)",",|cosx|gt(1)/(sqrt2)),(2+cosx+(1)/(sqrt2)",",|cosx|le(1)/(sqrt2)):}`
Thus, f(x) is discontinuous at `|cosx|=(1)/(sqrt2)` or
`x=(pi)/(4),(3pi)/(4),(5pi)/(4),(7pi)/(4)`