Free Skill check: Mean value theorem, L'Hopital, and local linearization Practice Problems • Learn To Be

The mean value theorem applies to functions defined on some closed interval

[a, b]

. What conditions must the function obey in order for the mean value theorem to apply?

What is the statement of the mean value theorem?

Choose 1 answer:

A
For all $c \in (a, b)$ , there exists some number $c' \in (a, c)$ such that $f'(c) = \dfrac{f(c') - f(a)}{c' - a}$
B
For all $c \in (a, b)$ , the following inequality holds: $\dfrac{f(c) - f(a)}{c - a} \le f'(c) \le \dfrac{f(b) - f(c)}{b - c}$
C
There exists a point $c \in (a, b)$ such that
$f'(c) = \dfrac{f(b) - f(a)}{b - a}$
D
There exists a point $c \in (a, b)$ such that $\dfrac{f(c) - f(a)}{c - a} = f'(c) = \dfrac{f(b) - f(c)}{b - c}$

Skill check: Mean value theorem, L'Hopital, and local linearization