Find the smallest and largest value of the function y = x ^ 2 + 4x + 4 on the interval [-3; 1].

y = x ^ 2 + 4x + 4;

1. Find the derivative of the given function:

y ‘= (x ^ 2 + 4x + 4)’ = 2x + 4;

2. Find the critical points:

2x + 4 = 0;

2x = -4;

x = -2;

3. Find the values of the function at the point and at the ends of the segment:

y (-3) = (-3) ^ 2 + 4 * (-3) + 4 = 1;

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

y (1) = 12 + 4 * 1 + 4 = 9;

Answer: min y (-2) = 0, max f (1) = 9.