Can someone tell me if my logic in answering the following questions is ok:(adsbygoogle = window.adsbygoogle || []).push({});

1. Suppose that f(x) and g(x) are convex on (a,b). Show that the functions h(x)=max[f(x), g(x)] is also convex on (a,b).

-I said that since f and g are convex their second derivatives are not equal to zero in (a,b) and then said since h is the max of f or g, that h also has a second derivative in (a,b) not equal to zero implying it is also convex.

2. Let f be differentiable on (a,b). Show that if f is convex if and only if for all x, y in (a,b): f(y)-f(x)>(y-x)f'(x)

-I'm at a loss on this one.

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# Convex functions

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