Find the largest and smallest value of the function y = x + 4 / x on the interval [1; 3].

y = x + 4 / x

Let’s find the derivative of the function:

y ‘= 1 – 4 / x2

Let’s find the extremum points, i.e. points at which y ’= 0:

1 – 4 / x2 = 0

(x2 – 4) / x2 = 0

x1 = -2

x2 = 2

at the point x3 = 0 the derivative of the function does not exist.

The gap [1; 3] only the point x2 = 2 belongs, therefore we consider the values of the function at the ends of the segment and at the point x2.

For x = 1, y = 5.

For x = 2, y = 4.

For x = 3, y = 13/3.

Thus, unaib = y (1) = 5, unaim = y (2) = 4.

Answer: unaib = 5, unaim = 4.