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

Question

Charles Anctil · Accepted Answer

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

In AP Calculus, you nearly always end up taking the values to the left and right of your target value and calculating based on them. There are occasionally additional requirements. x| f(x)1 | 3 | 2 | 5 | 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#

Paisley Johnson · Answer

undefined To find the instantaneous rate of change from a table, you need to locate two points that are very close together on the table. Then, calculate the change in the output variable divided by the change in the input variable between those two points. This will give you an approximation of the instantaneous rate of change at the specific input value corresponding to the two points. If you want a more precise calculation, you can make the interval between the two points even smaller. Ultimately, the instantaneous rate of change can be estimated by taking the limit as the interval approaches zero.