Question

sin x + cos x, 0< = x <= 2pi ,Find the extrema of the function on the given interval, and say where they occur

Answer 1

Find the derivative of the function, pretty easy. Set f' equal to 0, solve for x. That'll be your critical numbers on f(x). Use the First Derivative Test to figure out if these critical numbers result in a local max or a local min, or even neither!

Answer 2

When doing the FDT, if the interval goes from negative to positive, it'll be a local minimum. If from positive to negative, it'll be a local maximum.