BC 1
Mean Value Theorem
(1)
Name:
Let ƒ(x) = | x2 – 1|.
Do the hypotheses of the MVT hold on [0, 3]? Explain.
Do the conclusions of the MVT hold on [0, 3]? Explain.
Do the hypotheses of the MVT hold on [1, 3]? Explain.
Do the conclusions of the MVT hold on [1, 3]? Explain.
(2)
Does the MVT apply to g(x) = x1/3 on [0, 8]? Why or why not? Find all values of c that
satisfy the conclusions of the MVT.
(3)
Find all values of c which satisfy the MVT for h(x) = x3 + 6x + 2 on [–1, 3].
(4)
A car travels 102 miles in 3 hours. What does the MVT tell you?
IMSA
MVT. 1
F11
(5)
I made some hot chocolate last night. It was 185° F. The phone rang and I talked for a
while. Twenty minutes later, the temperature of my not-quite-so-hot chocolate was 120°.
What assumptions must be made to apply the Mean Value Theorem to this situation?
What does the MVT say about this situation? (Be specific to this case.)
(6)
An elevator starts at ground level at time t = 0 seconds. At t = 20 seconds, the elevator
has risen 100 feet. What does the Mean Value Theorem tell you about this situation?
(7)
Decide whether or not the hypotheses of the MVT hold for k(x) = 25 - x 2 on [–3, 5]. If
so, find all values of c that satisfy the theorem. If not, state why not.
(8)
A barrel is leaking water. When first measured at 2:03 pm, 20 gallons of water are in the
barrel. At 2:12 pm, only 5 gallons remain.
The Mean Value Theorem can probably be applied to this situation. If so, what
assumptions must be made? (Be specific to this situation.)
What may be concluded? (Be specific to this situation.)
IMSA
MVT. 2
F11