Question

For which interval is the average rate of change of f(x) negative?

A. From x=-4 to x=-1
B. From x=-3 to x=3
C. From x=0 to x=2.5
D. From x=3 to x=4.5

Answer 1

A negative changing rate in a curve is indicated by the negative gradient (slope). A copy of the graph with a negative gradient that tangent to the curve is shown below. This happen between
`x=0` and
`x=2.5`

Answer 2

Answer: The correct option is C.

Step-by-step explanation:

Reason for correct option:

From the given figure it is noticed that the graph do not turn on the interval [0,2.5]. As the value of a increases the value of y decreases, So the relation between x and y is negative and the rate of change is also negative. Therefore the option C is correct.

Reason for incorrect options:

From the figure it is noticed that the graph turns at least once in the interval [-4,-1] and [-3,3], it means the rate change varies in those intervals, therefore the option A and B are incorrect.

In the interval [3,4.5], the value of y increases as the value of x increases, therefore the relation between x and y is positive and rate of change is also positive. So the option D is also incorrect.