Question

Let f:rr be a function defined by f(x)=max{x,x3}. The set of all points, where f(x) is not differentiable, is

Answer 1

Answer:

f(x)=max{x,x3}

=⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪x;x3;x;x3;x<−1−1≤x≤00≤x≤1x≥1

∴f′(x)=⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪1;3x2;1;3x2;x<−1−1≤x≤00≤x≤1x≥1

⇒f is not differentiable at −1,0 and 1

Hence (d) is the correct answer