Question

Which function below has the smallest average rate of change from x=0 to x=2?

A) g(x)=5x
B) h(x)=2^x
C) f(x)= 1/4 • x^2

Answer 1

The function f(x) = 1/4 • x^2 has the smallest average rate of change from x=0 to x=2, which is 0.5.

Step-by-step explanation:

To find which function has the smallest average rate of change from x=0 to x=2, we must calculate the average rate of change for each function over this interval.

1. For g(x) = 5x, the average rate of change is calculated as:
   [g(2) - g(0)] / (2 - 0) = (5(2) - 5(0)) / 2 = 10 / 2 = 5.
2. For h(x) = 2^x, the average rate of change is:
   [h(2) - h(0)] / (2 - 0) = (2^2 - 2^0) / 2 = (4 - 1) / 2 = 3 / 2 = 1.5.
3. For f(x) = 1/4 • x^2, the average rate of change is:
   [f(2) - f(0)] / (2 - 0) = [(1/4)(2^2) - (1/4)(0^2)] / 2 = (1 - 0) / 2 = 1 / 2 = 0.5.

The function with the smallest average rate of change is f(x) = 1/4 • x^2 with an average rate of change of 0.5.