Objectives:
1. Be able to apply The Mean Value Theorem to various
functions.
Critical Vocabulary:
The Mean Value Theorem
Warm Up: Determine if Rolle’s Theorem can be applied. If it
can, find all values of c such that f’(c) = 0.
f(x) = x2 - 5x + 4; [1, 4]
If f is continuous on a closed interval [a, b] and
differentiable on the open interval (a, b), then there
exists a number c in (a, b) such that
f (b)  f (a)
f ' (c ) 
ba
Example 1: Given f(x) = 5 - (4/x), find all values of c in
the open interval (1,4) such that
f (4)  f (1)
f ' (c ) 
4 1
Example 2 (page 326 #24): Determine whether the Mean Value Theorem
can be applied to f on the closed interval [a, b]. If the Mean Value
Theorem can be applied, find all values of c in the open interval (a, b) such
that
f (b)  f (a)
f ' (c ) 
ba
Page 326-327 #19-27 odds, 33