Question: A function is called convex if it satisfies the following:

,

for any and any scalar with Show that the function in Question 2 above is convex using the following steps:

1. Show that the sum of convex functions is convex.
2. Define the function
   for any scalar, fixed constants Show that
   where u, v, and are as at the beginning of this question (Question 3) with .
3. Show that the function , t a scalar real number, is convex.
4. Explain how steps (a)-(c) can be put together to establish that the function in Question 2 is convex.

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