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Question

Let f: R → R be a function defined by f(x) = max {x, x3}, then-

A

f (x) is discontinuous at 3 points

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B

f (x) is not differentiable at 3 points

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C

f(x) is continuous at all points

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D

f (x) is not differentiable at x = 0

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Solution

The correct options are B f (x) is not differentiable at 3 points C f(x) is continuous at all points D f (x) is not differentiable at x = 0 y=x3 Clearly not differentiable at x= 0, ±1. 2nd method Solvingx3= x, we have x= 0, ±1 ∴ Max {x,x2}= x when x<-1 =x3 when -1 ≤ x ≤ 0 = x when 0 < x ≤ 1 =x3 when x < 1

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