Math miscellaneousHard

Question

If f(x) = , then

Options

A.f(x) is continuous at x = - π/2
B.f(x) is not differentiable at x = 0
C.f(x) is differentiable at x = 1
D.f(x) is differentiable at x = -3/2

Solution

f(x) = 0 = f (- π/2)
f(x) = cos = 0

Clearly, f (x) is not differentiable at x = 0 as f′( 0- ) = 0 and f′( 0+ ) = 1.
f (x) is differentiable at x = 1 as f′ ( 1- ) = f′ ( 1+ ) = 1.

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