Question

Compare the functions below. Which function has the greatest rate of change on the interval from x= π to x=3 π/2?

A. f(x)
B. g(x)
C. h(x)
D. All three functions have the same rate of change.

Answer 1

The function with the greatest rate of change on the interval from x= π to x=3 π/2 is function A.

Step-by-step explanation:

The rate of change is determined by the slope of the function. To compare the functions, we need to find the slopes or the derivatives. Let's calculate the derivatives of the functions and evaluate them at x = π and x = 3π/2.

A. f(x) = 3x - 2; f'(x) = 3

B. g(x) = -2x + 4; g'(x) = -2

C. h(x) = x - 3; h'(x) = 1

By evaluating the derivatives at the given x-values, we find that f'(x) = 3, g'(x) = -2, and h'(x) = 1. Therefore, function A has the greatest rate of change on the interval from x = π to x = 3π/2.