Question

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

Answer 1

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.