Rolle'S Theorem And The Mvt Worksheet 3.2 With Answers - Math 141e Calculus Maximus, Penn State School Page 5
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6Calculus Maximus
WS 3.2: Rolle’s Thm & MVT
=
⎧
0,
x
0
( )
( )
( )
( )
= ⎨
=
13. The function
is differentiable on
0,1 and satisfies
. However,
f x
f
0
f
1
−
< ≤
1
x
, 0
x
1
⎩
( )
its derivative is never zero on
0,1 . Does this contradict the Mean Value Theorem? Explain why or
why not.
14. Determine the values of a, b, and c such that the function f satisfies the hypothesis of the MVT on the
[ ]
interval
0,3 .
⎧
=
1,
x
0
⎪
( )
=
+
< ≤
f x
ax b
,
0
x
1
⎨
⎪
2
+
+
< ≤
x
4
x c
, 1
x
3
⎩
[
]
( )
15. Suppose that we know that
f x is continuous and differentiable on
6,15 . Let’s also suppose that
[
]
( )
( )
′
= − and that
≤
x ∈
we know that
f
6
2
f x
10
for all
6,15
. What is the largest possible value for
( )
f
15
?
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