Rolle'S Theorem And The Mvt Worksheet 3.2 With Answers - Math 141e Calculus Maximus, Penn State School Page 4
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6Calculus Maximus
WS 3.2: Rolle’s Thm & MVT
[ ]
( )
4
3
2
= −
+
+
+ on
11. (Calculator permitted) For
f x
x
4
x
8
x
5
0,5
(a) Determine if the MVT can be applied on the given interval. If so, find the value(s) guaranteed by
the theorem.
[ ]
(b) Find the equation of the secant line on
0,5
(c) Find the equation of the tangent line at any value of c found above.
[ ]
( )
(d) On your calculator, sketch a graph of
f x on
0,5 along with the secant and tangent line(s).
Sketch the graph below.
[ ]
( )
′
= . Using your
12. Let f satisfy the hypothesis of Rolle’s Theorem on an interval
, a b , such that
f c
0
knowledge of transformations, find an interval, in terms of a and b, for the function g over which
Rolle’s theorem can be applied, and find the corresponding critical value of g, in terms of c. Assume k
k > .
is a non-zero constant such that
0
( )
( )
( )
(
)
=
+
=
−
(a)
(b)
g x
f x
k
g x
f x k
New Interval:
New Interval:
New x-value:
New x-value:
( )
( )
( )
( )
=
=
(c)
g x
kf x
(d)
g x
f kx
New Interval:
New Interval:
New x-value:
New x-value:
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