Find the sum of the smallest and largest values of the function y = (2-x) (4-x) on the segment [1; 4]

We have a function: y = (2 – x) (4 – x) and the segment [1; 4].

Let’s find the value of the function for the given integer values of the argument:

When x = 1; y = (2 – 1) (4 – 1) = 1 * 3 = 3;

When x = 2; y = (2 – 2) (4 – 2) = 0 * 2 = 0;

When x = 3; y = (2 – 3) (4 – 3) = -1 * 1 = -1;

When x = 4; y = (2 – 4) (4 – 4) = -2 * 0 = 0;

We conclude that the largest value of the function on a given interval is the number 3, and the smallest is -1. We find their sum and thus answer the task question:

3 – 1 = 2.