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# 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)

16 Points
12 years ago

Dear Sanchit Gupta,

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

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

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

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

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

Hence option (a) is also wrong.

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

Hence option (c) is correct.

Please feel free to post as many doubts on our discussion forum as you can. If you find any question

Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We

are all IITians and here to help you in your IIT JEE preparation. All the best Sanchit Gupta

Regards,

nagesh