Find the largest and smallest value of the function y = x ^ 2 on a given interval: [-2; -1].

1. Let’s find the first derivative of the given function:

y ‘= (x ^ 2)’ = 2x.

2. Let us equate this derivative to zero and find the critical points:

2x = 0;

x = 0: 2;

x = 0.

Point x = 0 does not belong to the specified segment.

3. Find the value of the function at the ends of the given segment [-2; -one]:

y (-2) = (-2) ^ 2 = 4;

y (-1) = (-1) ^ 2 = 1.

The largest value of the function is at the point x = -2 and is equal to 4, the smallest value of the function is at the point x = -1 and is equal to 1.

Answer: the highest function value is 4, the lowest function value is 1.