Question

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

Answer 1

`(-3)`.

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 $x$})} \\ =\; & (f(-5) - f(2))/((-5) - 2) \\ =\; & (22 - 1)/(-7) \\ =\; & (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)`.