Question

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 answer:

Choose 1 answer:


(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]

Answer 1

It would be D

Explanation:

Answer 2

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

Explanation:

Let
`f(x) = x^(2)+10`, the average rate of change on the interval
`[a,b]` is represented by the definition of the secant line:

`\bar f = (f(b) -f(a))/(b-a)` (1)

Where:

`a`,
`b` - Lower and upper bounds, dimensionless.

`f(a)`,
`f(b)` - Function evaluated at lower and upper bounds, dimensionless.

Now we proceed to check each option:

A.
`a = -3`,
`b = 3`

`\bar f = (19-19)/(3-(-3))`

`\bar f = 0`

B.
`a = -4`,
`b = -1`

`\bar f = (11-26)/((-1)-(-4))`

`\bar f = -5`

C.
`a = -3`,
`b = 1`

`\bar f = (11-19)/(1-(-3))`

`\bar f = -2`

D.
`a = -1`.
`b = 2`

`\bar f = (14-11)/(2-(-1))`

`\bar f = 1`

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