Find the largest and smallest value of the function y = -3x ^ 2 in the range from -1 to 0

1. Find the first derivative of the function:

y ‘= (-3x ^ 2)’ = -6x.

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

-6x = 0;

x = 0: (-6);

x = 0.

3. Find the value of the function at this point and at the ends of the specified segment [-1; 0]:

y (0) = -3 * 0 ^ 2 = -3 * 0 = 0;

y (-1) = -3 * (-1) ^ 2 = -3 * 1 = -3.

The largest function value is 0 at x = 0, and the smallest function value is -3 at x = -3.

Answer: The largest function value is 0, and the smallest function value is -3.