If both f(x) and g(x) are differentible functions at x = x0 then the function defined as h(x) = Maximum [ f(x), g(x)] is(a)always differentiable at x=x0(b)never differentiable at x=x0(c)is differentiable at z=z0, provided f(x0)≠ g(x0)(d) cannot be differentiable at x=x0 if f(x0) = g(x0)

Dear Sanchit Gupta,

If f(x) = g(x), then h(x)=f(x), and h(x) is differentiable at x= x_o.

So options (b) and (d) are wrong.

Let f(x) and g(x) be to different.

Consider f(x) = g(x) at x = x_o, then

h(x) is not differentiable at x_o, since it will have a sharp edge at that point.

Hence option (a) is also wrong.

If f(x_o) ≠ g(x_o), then h(x) is differentiable at x_o, provided both f(x) and g(x) are differentiable at x_o, which is given.

Hence option (c) is correct.

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