Tribute to a very special woman...

The following was written by one of my daughters. It expresses what each of
us feels every day after six years...
A little boy walks by alone on the sidewa...
1 month ago
The answer is c = f((a+b)/2).
ReplyDeleteSince f is continuous and increasing, it has an inverse function g. By turning the graph sideways, we see that the area A(c) is given by the following equation.
A(c) = int (f(a) to c) [g(x)  a] dx + int (c to f(b)) [b  g(x)] dx.
Using the fundamental theorem of calculus,
A'(c) = 2g(c)  a  b,
so the minimum area occurs when A'(c) = 0, or when g(c) = (a+b)/2, which is equivalent to c = f((a+b)/2).