Find the largest value of the function y = 9cosx + 16x − 8 on the segment [−3π 2; 0]

To determine the maximum value of the function, we define its derivative.

Y ‘= -9 * SinX + 16.

Let us equate the derivative to zero and determine the critical points.

-9 * SinX + 16 = 0;

SinX = 16/9.

The equation has no roots.

Then we determine the value of the function at the ends of the interval [-3π / 2; 0].

Y (-3π / 2) = 9 * Cos (-3π / 2) + 16 * (-3π / 2) – 8 = 0 – 24 * π – 8 = – (27 * π + 8);

Y (0) = 9 * Cos0 + 16 * 0 – 8 = 9 + 0 – 8 = 1.

Answer: The largest value is Y (0) = 1.