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 .