Question

What is correct about mean value theorem?

• A. It states that given a planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.
• B. It tells us when certain values for the derivative must exist.
• C. Both A and B
• D. Only B

Answer 1

Answer: (C)

Both A and B

The mean value theorem states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.

This theorem is used to prove statements about a function on an interval starting from local hypotheses about derivatives at points of the interval.

More precisely, if $f$ is a continuous function on the closed interval $[a,b]$, and differentiable on the open interval $(a,b)$, then there exists a point $c$ in $(a,b)$ such that:

$f^{\prime }\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$