If both f(x) , & ,g(x) are differentiable functions at x = x_0, t… - Vidyadip

MCQ

If both $f(x)\, \& \,g(x) $ are differentiable functions at $x = x_0$, then the function defined as, $h(x) =$ Maximum $ \{f(x), g(x)\} :$

A
is always differentiable at $x = x_0$
B
is never differentiable at $x = x_0$
✓
is differentiable at $x = x_0$ provided $f(x_0) \ne g(x_0)$
D
cannot be differentiable at $x = x_0$ if $f(x_0) = g(x_0) .$

✓

Answer

Correct option: C.

is differentiable at $x = x_0$ provided $f(x_0) \ne g(x_0)$

c
Consider the graph of $h(x) = max(x, x^2)$ at $x = 0$ and $x = 1$

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