Find the largest and smallest values of the function y = √x on the segment [a: b]: [1: 9] [5:25].

We have a function:

y = x ^ (1/2).

ODZ functions are all non-negative numbers.

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

y ‘= 1/2 * x ^ (- 1/2).

The derivative of the function cannot be equal to zero, since there is one in the numerator of the fraction. The function has no critical points.

Find and compare the values of the function at the boundaries of the interval:

1) y (1) = 1 is the smallest value.

y (9) = 3 is the largest value.

2) y (5) = 5 ^ (1/2) is the smallest value.

y (25) = 5 is the largest value.