Question

Which of the following statements is true?

А.At approximately x = 4.39, the rate of change of fis equal to the rate of change of g.
В.As x increases, the rate of change of fexceeds the rate of change of g.
C.For every value of x, the rate of change of g exceeds the rate of change of f.
D.As xincreases, the rate of change of g exceeds the rate of change of f.

Answer 1

The statement that is true is Option B: As x increases, the rate of change of f exceeds the rate of change of g.

Step-by-step explanation:

The statement that is true is Option B: As x increases, the rate of change of f exceeds the rate of change of g.

In calculus, the rate of change is represented by the derivative. If the derivative of f is greater than the derivative of g, it means that the rate of change of f is greater than the rate of change of g. In other words, as x increases, the function f is changing at a faster rate than the function g.

For example, if f(x) = x^2 and g(x) = x, the derivative of f is f'(x) = 2x, and the derivative of g is g'(x) = 1. As x increases, the value of f'(x) = 2x increases at a faster rate than the value of g'(x) = 1.