Question

The graph of the derivative of a function, f, is shown. Use the graph to determine the interval on which f is increasing.

A. (-∞, 2)
B. (2, ∞)
C. (-∞, ∞)
D. (-1, ∞)
E. (-∞, 1)

Answer 1

B)
`(2,\infty)`

Explanation:

Since we are given the graph of
`f'(x)`, this gives us the value of the derivative, or the rate of change, of
`f(x)` given an x-value. For
`f(x)` to be increasing, then
`f'(x) > 0`, which is a positive rate of change. As you may have noticed, when
`x > 2`, the value of
`f'(x)` is positive. This means that f increases on the interval
`(2,\infty)`, or answer B.