F(x)= x^2 + 10f(x)=x 2

+10f, left parenthesis, x, right parenthesis, equals, x, squared, plus, 10

Over which interval does fff have a positive average rate of change?

Choose 1

Choose 1

(Choice A)

A

[-3,3][−3,3]open bracket, minus, 3, comma, 3, close bracket

(Choice B)

B

[-4,-1][−4,−1]open bracket, minus, 4, comma, minus, 1, close bracket

(Choice C)

C

[-3,1][−3,1]open bracket, minus, 3, comma, 1, close bracket

(Choice D)

D

[-1,2][−1,2]

The option D represents an interval with a positive average rate of change.

Step-by-step explanation:

Let , the average rate of change on the interval is represented by the definition of the secant line:

(1)

Where:

, - Lower and upper bounds, dimensionless.

, - Function evaluated at lower and upper bounds, dimensionless.

Now we proceed to check each option:

A. ,

B. ,

C. ,

D. .

The option D represents an interval with a positive average rate of change.

the answer to the question is a  

it has the same slope and the same y-intercept.