Find the range of values of the function y = x ^ 2 – 6x-13, where x belongs to [-2; 7]

We have a function:

y = x ^ 2 – 6 * x – 13.

The range of values of the function on the interval is found from finding the smallest and largest values.

Let’s find the critical points of the function.

Find the derivative of the function:

y ‘= 2 * x – 6;

y ‘= 0;

2 * x – 6 = 0;

x = 3 – critical point.

Let’s find the largest and smallest values of the function on the interval:

y (-2) = 4 + 12 – 13 = 3;

y (3) = 9-18-13 = -22;

y (7) = 49-42-13 = -6;

The range of values of the function on the interval is the interval [-22; 3].