Finding local extrema

Question

Consider the family of functions f(x)= a cos +(sinx)^2, where the parameter a varies over the interval (0,3). The locations of the local extrema of functions in this family depend on the parameter of a. Find and classify (as a max or min) all local extrema of the functions f(x)= acosx + (sinx)^2 in the interval (-1,2) and make sure to explain how your answers depend on the value of a.

Answer 1

This question is best answered by first going to DESMOS and graphing the function for several values of a.

There is a maximum when cos x=a/2 and there are extrema where sin x=0.

The size of the extrema depends on a.