Find the largest and smallest value of the linear function y = -x-1 on the interval (-4; 5).

The solution of the problem.

1. Find the derivative of the function y (x) = -x – 1.

y ‘(x) = -1.

2. The derivative function exists and does not vanish on the entire numerical interval, therefore, the function y (x) = -x – 1 has no critical points.

3. Find the one-sided limit of the function at x -> -4 + 0.

limx -> – 4 + 0y (x) = 3.

4. Let us find the one-sided limit of the function as x -> 5 – 0.

limx-> 5-0y (x) = -6.

Answer. The highest value of the function at the given open interval is equal to 3. The smallest value of the function at the given open interval is -6.