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2 votes
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]

2 Answers

5 votes

Answer:

It would be D

Explanation:

User Shannon Cornish
by
8.1k points
5 votes

Answer:

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.

User Phimuemue
by
8.5k points
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