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Let $f$, $g$ and $h$ be real valued functions defined as follows: $f(x) = x(1 − x)$, $g(x) = x/2$ and $h(x) = min(f(x), g(x)) $ with $0

A) continuous and differentiable

B) is differentiable but not continuous

C) is continuous but not differentiable

D) is neither continuous nor differentiable

How to go about this? $ h(x)= \begin{cases} g(x) & \text{ if } 0

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    Did you try plotting the function? Do you think it is continuous? Do you think it is differentiable? By the way, what you wrote is indeed correct. – 2017-02-22
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    In these type of questions, always try to draw the graphs of $f(x)$ and $g(x)$ and then shade the part of the graphs which is lesser, this will give you the graph oh $h(x)$. For differentiability, you can then see the corner points. – 2017-02-22

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From the graph we can clearly see that $h(x)$ is continuous everywhere but not differentiable at $x=0.5$

enter image description here

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    Note to OP: "Seeing from a graph" is not a valid method for solving mathematical problems. It's useful to see the solution, but the solution must then still be *proven*. – 2017-02-22