Question

If both f(x) and 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
• B. Is never differentiable at
• C. Is differentiable at provided
• D. Cannot be differentiable at if

Answer 1

The correct option is C Is differentiable at provided

Consider the graph of f(x) = max(sinx, cosx), which is non-differentiable at $x=\frac{\pi }{4}$, hence statement (A) is false. From the graph y = f(x) is differentiable at $x=\frac{\pi }{2}$, hence statement (B) is false.
Statement (C) is false
Statement (D) is false as consider $g\left(x\right)=max(x,x^2)$ at x = 0, for which $x=x^2$ at x = 0, but f(x) is differentiable at x = 0.