Deck 4: Extension B: Applications of Differentiation

Question 1

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)

Answer 1

Question 2

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) -7
B) -8, -6
C) -8, -7
D) -6

Answer 2

-7

Question 3

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

Answer 3

Question 4

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) ,

Question 5

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) c=0.7
B) c=6.0
C) c=3.0
D) c=57
E) c=3.9
F) c=0
G) c=1.3
H) c=0.1

Question 6

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.

Question 7

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)

Question 8

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) -6, -4
B) -5, -4
C) -6
D) -5