1. The problem statement, all variables and given/known data Find the extrema of over [0,pi/2] ρsinθ + cosθ = f(θ), where ρ is a constant 2. Relevant equations Extrema occur at critical points and global extrema occur at end points. 3. The attempt at a solution f(0) = 1 f(pi/2) = ρ f'(θ) = ρcosθ - sinθ = 0 ρcosθ = sinθ. θ = pi/4. This seems to maximize the original function because geometrically, the largest triangle is constructed on the unit circle by making the two legs (the cosine and sine functions) equal in length. f(pi/4) = √2ρ > ρ. Or is θ = arctan(ρ)?