Question

F(x) = x^2-3 What is the average rate of change on the interval [-5, 2] ?

Answer 1

Answer:

$(-3)$.

Step-by-step explanation:

Over this interval, the change in the value of this function is:

$f(-5) - f(2) = 22 - 1 = 21$.

The corresponding change in the value of $x$:

$(-5) - 2 = -7$.

The average rate of change of function $f$ over this interval is equal to the change in the function value divided by the corresponding change in $x$:

$\begin{aligned}& (\text{average rate of change}) \\ =\; & \frac{(\text{change in function value})}{(\text{change in x })} \\ =\; & \frac{f(-5) - f(2)}{(-5) - 2} \\ =\; & \frac{22 - 1}{-7} \\ =\; & \frac{21}{-7} \\ =\; & -3\end{aligned}$.

Thus, the average rate of change of $f(x) = x^{2} - 3$ over the interval $[-5,\, 2]$ would be $(-3)$.