Mathematics

Problem

For a family of regions whose area is given by

A(k)=\displaystyle\int_{0}^{k}[f(x)-g(x)]\,dx

with

f(x)\ge g(x)

and both

f

and

g

continuous, what analytic condition must the parameter

k

(with

0<k<c

) satisfy if

A(k)

has an interior extremum at that value of

k