Determine the points at which the graph of the function has a horizontal tangent line. f(x) = x² - 8

Solution:

Given, function f(x) = x² - 8

We have to find the points at which the graph of the function has a horizontal tangent line.

A point on a function will have a horizontal tangent line where the first derivative is zero.

Thus, f’(x) = 2x

Now, f’(x) = 0

2x = 0

x = 0

Put x = 0 in f(x)

f(16) = (0)² - 8 = -8

Therefore, the point is (0, -8).

Determine the points at which the graph of the function has a horizontal tangent line. f(x) = x² - 8

Summary:

The points at which the graph of the function has a horizontal tangent line. f(x) = x² - 8 is (0, -8).