Find the smallest and largest values of the function: y = cos x on the segment [-2π / 3; π / 2].

We have a function:

y = cos x.

To find the smallest and largest values of the function on the interval, we find its derivative:

y ‘= -sin x.

Let us equate the derivative to zero – find the critical points:

sin x = 0;

x = π * N, where N is an integer.

x = 0 is the critical point of the function included in the interval from the conditions of the problem.

Let us find and compare the values of the function from the boundaries of the interval and the critical point:

y (-2 * π / 3) = cos (-2 * π / 3) = -1/2 – the smallest value.

y (0) = cos 0 = 1 is the largest value.

y (π / 2) = cos (π / 2) = 0.