Find the largest and smallest value of the function y = -3x + 5 on the interval [-5; 7].

Let’s find the first derivative of this function:

y ’(x) = (3 * x + 5)’ = 3.

Equating the derivative to zero:

3 ≠ 0, therefore, there are no global extrema.

Let’s calculate the value of the function at the ends of the segment, that is, for x = -5, x = 7:

y (-5) = 3 * (-5) + 5 = -15 + 5 = -10.

y (7) = 3 * 7 + 5 = 26.

Answer: the largest value of the function ymax = 26, the smallest value of the function ymin = -10.