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Table Quiz
Names:
Show all work/Explain clearly.
Turn in one copy per table. Each person at the table receives the same grade.
1.
The graph of a function f is shown below at
the right.
y
a. Does f satisfy the hypothesis of the
MVT on [a, b]? Explain clearly.
x
a
b.
Does f satisfy the conclusion of the MVT?
d
b
, If not, explain carefully wny not
referring to the above graph. If so, there is still a number c between a and b that satisfies the
conclusion of the MVT. Mark this value of c (approximately) on the x-axis of the graph above.
c.
Does f satisfy the hypothesis of the IVT?
If so, state why. If not, state what
part of the hypothesis of the IVT  does not satisfy?
2.
16
 3x .
x
a. Does g satisfy the hypotheses of the MVT on [–4, –1]?
Let g  x  
.
b. Find all value(s) of c that satisfy the conclusions of the MVT on the interval [–4, –1].
Calculator Allowed
Table Quiz
Names:
Show all work/Explain clearly.
Turn in one copy per table. Each person at the table receives the same grade.
2. For each of the following conjectures, decide if it is true or false. For the true statements, give some
coherent justification for the statement using complete sentences. For the false statement, draw or
otherwise describe a function f which provides a counterexample, and explain why it does. Always
assume that [a, b] implies that a  b .
a. Let a function f on [a, b] be given which is differentiable on (a, b) and continuous on [a,b]. If
f ( s)  f (r )
c  (a, b) , then there are r , s  [a, b] such that r < c < s and f (c) 
.
sr
b. Let f be a function with domain [a, b] , then f has a maximum and a minimum value on [a,b].
c. Let f be a continuous function with domain (a, b) , then f has a maximum and a minimum
value on (a,b).
d. Suppose that f is differentiable on (a, b) . Then for r , s  (a, b) and a y between f (r ) and f ( s)
there is some c  (r , s ) such that f (c)  y .
Calculator Allowed
Table Quiz
Names:
Show all work/Explain clearly.
Turn in one copy per table. Each person at the table receives the same grade.
3.
Ship A is traveling due east away from Lighthouse
Ship B
Rock at a speed of 18 kilometers per hour (km/hr).
Ship B is traveling due south toward Lighthouse
Rock at a speed of 12 km/hr. Let x be the distance
y
between Lighthouse Rock and Ship A at time t, and
let y be the distance between Lighthouse Rock and
Ship B at time t, as shown in the figure at the right.
Find the rate of change, in km/hr, of the distance
Lighthouse x
between Ship A and Ship B when x is 6 km and
y is 8 km.
Rock
N
Ship A