Question

How do you find the instantaneous rate of change from a table?

Answer 1

You approximate it by using the slope of the secant line through the two closest values to your target value.

Explanation:

Sometimes there are more requirements, but in AP Calculus you almost always end up taking the values to the left and right of your target value and calculating based on them.

x | f(x)
1 | 3
2 | 5
3 | 4
4 | 9

From the "table" we'd approximate the following:
`f'(2)\approx(f(3)-f(1))/(3-1) = 1/2`
`f'(3)\approx(f(4)-f(2))/(4-2) = 4/2=2`

For 1 and 4 we'd have no choice but to do this:
`f'(1)\approx(f(2)-f(1))/(2-1) = 2/1=2`
`f'(4)\approx(f(4)-f(3))/(4-3) = 5/1=5`