Question

If ab and f(a)lf(b), then there is some value of c between a and b for which . Choose the correct answer below.

A) Intermediate Value Theorem
B) Fundamental Theorem of Calculus
C) Mean Value Theorem
D) Ratio Test

Answer 1

The correct answer is the Mean Value Theorem, which relates the rate of change of a continuous and differentiable function to the average rate of change over an interval.

Step-by-step explanation:

If ab and f(a) f(b), then there is some value of c between a and b for which f'(c)=(f(b)-f(a))/(b-a). The correct answer to this question is C) Mean Value Theorem.

This theorem is essential in calculus and states that if a function is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there is at least one point c in the interval (a, b) where the instantaneous rate of change (derivative) of the function is equal to the average rate of change over the interval [a, b].