Stewart_Calc_7ET ch04sec02
MULTIPLE CHOICE
1. Find the number c that satisfies the conclusion of the Mean Value Theorem on the given
interval.
,
a.
b.
c.
d.
e.
None of these
2. The function satisfies the hypotheses of Rolle’s Theorem on the
interval . Find all values of c that satisfy the conclusion of the theorem.
a.
–5, –4
b.
–5
c.
–6, –4
d.
–6
3. The function satisfies the hypotheses of Rolle’s Theorem on the interval
. Find all values of c that satisfy the conclusion of the theorem.
a.
b.
c.
d.
25
4
4. The function satisfies the hypotheses of Rolle’s Theorem on the interval
. Find all values of c that satisfy the conclusion of the theorem.
a.
b.
1
c.
d.
5. The function satisfies the hypotheses of Rolle’s Theorem on the interval
. Find all values of c that satisfy the conclusion of the theorem.
a.
b.
c.
d.
6. The function satisfies the hypotheses of the Mean Value Theorem on the
interval . Find all values of c that satisfy the conclusion of the theorem.
a.
–8, –6
b.
–8, –7
c.
–7
d.
–6
7. The function satisfies the hypotheses of the Mean Value Theorem on the
interval Find all values of c that satisfy the conclusion of the theorem.
a.
b.
c.
d.
8. How many real roots does the equation have in the interval ?
a.
at most five real roots
b.
no real roots
c.
at most one real root
d.
at most two real roots
e.
at most three real roots
9. Verify that the function satisfies the three hypotheses of Rolle’s Theorem on the given
interval. Then find all numbers c that satisfy the conclusion of Rolle’s Theorem.
,
a.
None of these
b.
,
c.
,
d.
,
e.
,
10. Verify that the function satisfies the three hypotheses of Rolle’s Theorem on the given
interval. Then find all numbers c that satisfy the conclusion of Rolle’s Theorem.
a.
b.
c.
d.
e.
MULTIPLE RESPONSE
1. Use the graph of to estimate the values of c that satisfy the conclusion of the Mean Value
Theorem for the interval [0, 7].
Select all that apply.
a.
b.
c.
d.
e.
f.
g.
h.
NUMERIC RESPONSE
1. At 4:00 P.M. a car’s speedometer reads 25 . At 4:15 it reads 72 . At some time
between 4:00 and 4:15 the acceleration is exactly x . Find x.