determine whether the following statement is true or false, and explain why. the derivative of f(x)…

determine whether the following statement is true or false, and explain why. the derivative of f(x) represents the instantaneous rate of change of y = f(x) with respect to x. choose the correct answer below. a. the statement is false because the derivative is the average rate of change of x with respect to y = f(x). b. the statement is true because the definition of the instantaneous rate of change for a function f at x is the same as the definition of the derivative of a function f at x. c. the statement is false because the derivative is the instantaneous rate of change of x with respect to y = f(x). d. the statement is false because the derivative is the average rate of change of y = f(x) with respect to x.

determine whether the following statement is true or false, and explain why. the derivative of f(x) represents the instantaneous rate of change of y = f(x) with respect to x. choose the correct answer below. a. the statement is false because the derivative is the average rate of change of x with respect to y = f(x). b. the statement is true because the definition of the instantaneous rate of change for a function f at x is the same as the definition of the derivative of a function f at x. c. the statement is false because the derivative is the instantaneous rate of change of x with respect to y = f(x). d. the statement is false because the derivative is the average rate of change of y = f(x) with respect to x.

Answer

Brief Explanations:

The derivative of a function $y = f(x)$ represents the instantaneous rate of change of $y$ with respect to $x$, not the average rate of change. The average rate of change is calculated over an interval, while the derivative is the limit as the interval size approaches zero.

Answer:

A. The statement is false because the derivative is the average rate of change of $y = f(x)$ with respect to $x$.