Big Online Courses Have a Problem. Here’s How We Tried to Fix It.

The Problem Here is some personal prejudice: I don’t love online courses. I
love learning in community, even in online communities, but online courses
rare...
4 weeks 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).