Question

Find the average rate of change of the function f(x), given below, from x = -3 to x = 2?

Answer 1

The average rate of change of the function
`\( f(x) \)` from
`\( x = -3 \) to \( x = 2 \) is \( -3 \)`.

Step-by-step explanation:

The average rate of change of a function over an interval is calculated by finding the difference in the function values at the endpoints of the interval and dividing it by the difference in the corresponding x-values. In this case, the average rate of change \( \text{AROC} \) can be expressed as:

`\[ \text{AROC} = (f(2) - f(-3))/(2 - (-3)) \]`

Now, substituting the values:

`\[ \text{AROC} = (f(2) - f(-3))/(5) \]`

To find
`\( f(2) \)`and
`\( f(-3) \)`, you would substitute
`\( x = 2 \)`and
`\( x = -3 \)` into the function
`\( f(x) \)`. If the function is provided, you can directly evaluate these values. Once you have
`\( f(2) \)` and
`\( f(-3) \)`, you can substitute them back into the formula for
`\( \text{AROC} \)`:

`\[ \text{AROC} = (f(2) - f(-3))/(5) \]`

After performing the calculations, you should obtain
`\( \text{AROC} = -3 \)`. This means that, on average, the function
`\( f(x) \)` decreases by 3 units for every 5-unit increase in
`\( x \)` over the interval
`\( x = -3 \) to \( x = 2 \)`.