Question

Determine whether the statement is true or false. If f '(x) > 0 for 6 < x < 10, then f is increasing on (6, 10).

Answer 1

The statement is true.

Explanation:

The first derivative of a function at a point represents the slope of the tangent line of the function at that point, thus it allow us to tell if the function is increasing or decreasing.

Analyzing given information.

We are given that
`f'(x) >0` for 6 < x < 10. Since the derivative represents the slope, we know that the slope of the function f(x) is positive for all values of x between 6 and 10.

Since the slope is positive, we can tell that the function f(x) is increasing on the interval from 6 to 10, thus the statement is true.