Question

Use the image to answer the question.

A coordinate plane for f of x versus x.
▼Click for Long Desc
The x-axis ranges from 0 to 6 in increments in unit increments. The vertical axis represents f of x ranging from negative 2 to 3 in unit increments. A line passes through the coordinates left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 1 comma 1 right parenthesis, left parenthesis 3 comma 0 right parenthesis, left parenthesis 4 comma negative 0 point 5 right parenthesis, left parenthesis 5 comma negative 0 point 5 right parenthesis, and left parenthesis 6 comma 0 right parenthesis.

Given the graph of f(x)
, on which interval is the average rate of change the greatest?

(1 point)

The function has the greatest average rate of change over the interval [5,6]
.

The function has the greatest average rate of change over the interval [0,1]
.

The function has the greatest average rate of change over the interval [4,5]
.

The function has the greatest average rate of change over the interval [1,4]
.
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Answer 1

Compute the average rates:

- [5,6]: (f(6) − f(5)) / (6−5) = (0 − (−0.5)) / 1 = 0.5
- [0,1]: f(0) lies on line from (−2,0) to (1,1): f(0)=2/3, so (f(1)−f(0)) /1 = (1−2/3)=1/3 ≈0.333
- [4,5]: (−0.5 − (−0.5)) /1 = 0
- [1,4]: (−0.5 − 1) /3 = −0.5

Largest average rate is 0.5 on [5,6]. So the correct interval is [5,6].