Calculate the average rate of change of the given function f over the intervals [a, a + h] where h = 1, 0.1, 0.01, 0.001, and 0.0001

Question

f(x)= x^2/ 4; a=1

h=1 ___

h = 0.1. ___

h = 0.01. ___

h = 0.001. ___

h = 0.0001 ___

Answer 1

Average rate of change of a function, as opposed to instantaneous rate of change, can be calculated by using the good old-fashioned slope formula from, like, 7th grade: (y₂ - y₁) / (x₂ - x₁).

f(1) = 1/4 , so use (1 , 1/4) for (x₁ , y₁)

The question asks you to use x₂ = 2 , then 1.1 , then 1.01 etc.