Question

What is the average rate of change for the function f(x)=4x^2-2 on the interval [4, 3]?

A) -20
B) 3
C) -60
D) 30

Answer 1

The average rate of change for the function f(x) = 4x^2 - 2 on the interval [4, 3] is 32.

Step-by-step explanation:

The average rate of change for a function is calculated by finding the slope of the secant line between two points on the function. In this case, we want to find the average rate of change of the function f(x) = 4x^2 - 2 on the interval [4, 3].

We can find the slope of the secant line using the formula: average rate of change = (f(3) - f(4))/(3 - 4). Plugging in the values, we get: average rate of change = (4(3)^2 - 2 - 4(4)^2 + 2)/(3 - 4).

Simplifying further, we get: average rate of change = (34 - 66)/(-1) = -32/(-1) = 32. Therefore, the average rate of change for the function on the interval [4, 3] is 32.