Question

The function f is defined by f(x) = 2x34x²+1. The application of the Mean Value Theorem to ƒ on the interval 1 < x < 3 guarantees the existence of a value c. where 1 A.0

B.9
C.10
D.14
E.16

Answer 1

The question is incorrect as it provides an incomplete function for the application of the Mean Value Theorem, and it does not directly relate to continuous probability functions as suggested by the context provided.

Step-by-step explanation:

The question appears to be mistaken as it does not provide the exact function definition nor a clear context for applying the Mean Value Theorem. However, when considering the application of the Mean Value Theorem to a function on a specific interval, it guarantees the existence of at least one number c in the open interval (a, b) such that the instantaneous rate of change (derivative) at c is the same as the average rate of change (slope of the secant line) over the interval [a, b]. In a continuous probability function context, such as f(x) being equivalent to a probability density function, the theorem doesn't directly apply since probability functions and their properties can differ significantly from functions analyzed in the Mean Value Theorem application.