1. The problem statement, all variables and given/known data This problem comes from a practice test that I am reviewing before my final. My main confusion comes from the mathematical implication of the integral being an extremum. The first two parameters are y(x=0) = 0 and y(x = π/2) = 1. The third says the integral from 0 to 1 of ∫[ (dy/dx)2 - y2 ]dx is an extremum. 2. Relevant equations N/A 3. The attempt at a solution Clearly, the first two parameters are easily solved by y = sin(x). However, this third bit of information is very confusing to me. I first considered, in 1 dimension the first derivative of a function at an extremum is zero, and thus perhaps plugging in zero for dy/dx. That didn't seem right so I attempted to solve the integral, but couldn't figure out the first part to solve. Thirdly, I tried plugging in sin(x) and see what could be achieved, with a final result of something like .5-.27 = extremum (integral of sin2(x) from zero to one is the .27.) If possible, the guidance I am looking for is how to think about mathematically the fact that the the integrand, involving dy/dx is related to the extremum. Thanks. Sorry if the formatting is off, first post here.