Find the largest and smallest value of the function y = √x – 4, on the segment [5; 8].

Given a function:

y = (x – 4) ^ (1/2).

To find the largest and smallest values of the function, we find its derivative:

y ‘= 1/2 * (x – 4) ^ (- 1/2).

As you can see, there are no critical points of the function, but the derivative is positive for all x from the domain of definition, which means that the function increases in all domains of definition and in this interval in particular.

Means:

ymin = y (5) = (5 – 4) ^ (1/2) = 1;

ymax = y (8) = (8 – 4) ^ (1/2) = 2.