Find the range of values of the function Y = -3x-6x + 5 if x belongs to [-2; 1].

We have a function:

y = -3 * x ^ 2 – 6 * x + 5.

Let’s find its largest and smallest values on the segment and, accordingly, define the range of values on the interval:

Find the derivative:

y ‘= -6 * x – 6;

Let’s find the critical point:

-6 * x – 6 = 0;

x = -1 – critical point.

We find the values of the function from the critical point and the boundaries of the interval:

y (-2) = -3 * 4 – 6 * (-2) + 5 = 5;

y (-1) = -3 * 1 – 6 * (-1) + 5 = 8;

y (1) = -3 * 1 – 6 * 1 + 5 = -4;

We see that the range of values of the function on the interval is [-4; eight].