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Andrew [12]
2 years ago
13

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

Mathematics
1 answer:
Zielflug [23.3K]2 years ago
5 0

Answer:

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

Step-by-step 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 = \frac{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 = \frac{19-19}{3-(-3)}

\bar f = 0

B. a = -4, b = -1

\bar f = \frac{11-26}{(-1)-(-4)}

\bar f = -5

C. a = -3, b = 1

\bar f = \frac{11-19}{1-(-3)}

\bar f = -2

D. a = -1. b = 2

\bar f = \frac{14-11}{2-(-1)}

\bar f = 1

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

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