Consider the function

Find the minimum value of such that for all .

For this problem, first we want to find where the function has a minimum. Then, we’ll set this minimum equal to 24 to solve the problem.

To find the minimum we take the derivative of ,

Setting this equal to 0 we have

So, has a minimum at this value of . Now we plug this value of into and set it equal to 24 (so that at its minimum).

Thus, for all .