A find the critical points of the following function on the

A. find the critical points of the following function on the given interval B. Use a graphing utility to determin whether the critical points correspond to local maxima, and local minima, or neither. C. Find the absolute maximum and minimum values on the given interval.

f(theta)=2sin(theta)+cos(theta); [-2pi,2pi]

Identify all the critical points.

Identify all the critical points that are local minima.

Identify all the critical points that are local maxima.

Identify all the critical points that are not associated with local maxima and minima.

Identify the absolute maximum and minimum values both by value, and what x equals at this point.

Solution

f() = 2 sin() +cos()

f¹() = 2cos() - sin()

f¹¹ () = -2sin() -cos()

to find extreme points f¹¹ ()=0

-2sin()-cos()=0

-2sin()=cos()

tan() = -1/2

() = -26.5 means only maximum value exist

substitue value in f() we get 0.89