Question

Consider the functionf(x) = x² + 1 and find the following:

a) The average rate of change between the points(-1, f(-1)) and(4, f(4)).
a){f(4) - f(-1)}/{4 - (-1)} a){f(4) - f(-1)}/{4 - (-1)} b){f(a) - f(b)}/{a - b}
c){f(-1) - f(4)}/{-1 - 4}
d){f(b) - f(a)}/{b - a}

Answer 1

The average rate of change of the function f(x) = x² + 1 between the points (-1, f(-1)) and (4, f(4)) is calculated using the formula {f(4) - f(-1)}/{4 - (-1)}, which simplifies to 3.

Step-by-step explanation:

To find the average rate of change of the function f(x) = x² + 1 between the points (-1, f(-1)) and (4, f(4)), you would apply the formula for the average rate of change, which is the change in the function values over the change in x values. Specifically, you would compute {f(4) - f(-1)}/{4 - (-1)}.

First, evaluate the function at x = -1 and x = 4:

• f(-1) = (-1)² + 1 = 1 + 1 = 2
• f(4) = (4)² + 1 = 16 + 1 = 17

Next, substitute these values into the average rate of change formula:

{f(4) - f(-1)}/{4 - (-1)} = {17 - 2}/{4 - (-1)} = {15}/{5} = 3

Therefore, the average rate of change of the function between the points (-1, f(-1)) and (4, f(4)) is 3.