Find the difference between the smallest and largest values of the function y = x * x + 4 on the segment [-3; 2].

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

y ‘= (x ^ 2 + 4)’ = 2x ^ (2 – 1) + 0 = 2x.

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

2x = 0;

x = 0.

3. Find the value of the function at this point and at the ends of the specified segment [-3; 2]:

y (0) = 0 ^ 2 + 4 = 0 + 4 = 4;

y (-3) = (-3) ^ 2 + 4 = 9 + 4 = 13;

y (2) = 2 ^ 2 + 4 = 4 + 4 = 8.

The smallest function value is 4 and the largest function value is 13.

4. Find the difference between the smallest and largest values of the function:

13 – 4 = 9.

Answer: 9.