Find the largest value of the function y = 7sin x on the interval (-п / 2; 0)

Find the largest value of the function y = 7 * sin x on the interval (-pi / 2; 0).

1) First, we find the derivative of the function.

y ‘= (7 * sin x)’ = 7 * sin ‘x = 7 * cos x;

2) Let us equate the derivative of the function to 0.

7 * cos x = 0;

cos x = 0;

x = 2 * pi * n, where n belongs to Z;

x (0) = 2 * pi * 0 = 0 – belongs to the segment of the interval (-pi / 2; 0);

x (1) = 2 * pi * 1 = 2 * pi – does not belong to the segment in the interval (-pi / 2; 0);

x (-1) = 2 * pi * (-1) = -2 * pi – does not belong to the segment in the interval (-pi / 2; 0);

3) y (0) = 7 * sin 0 = 7 * 0 = 0;

y (-pi / 2) = 7 * sin (-pi / 2) = -7 * sin (pi / 2) = -7 * 1 = -7.

Answer: y max = 0.