Question

Let f: $R\to R$ be a function defined by $f\left(x\right)=Max\{x,x^3\}$ then

• A. f (x) is discontinuous at 3 points
• 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

Answer 1

Answer: (B), (C), (D)

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


Clearly not differentiable at $x=0,\pm 1$
$2^{nd}$ method
Solving $x^3=x$, we have $x=0,\pm 1$
$\therefore Max\{x,x^2\}=x$ When x < -1
$=x^3$ when $-1\le x\le 0$
=x when 0 < $x\le 1$
=x^3 when x > 1