Calculus Writing Assignment: Mean Value and Rolle's Theorems Each problem is worth 5 points. Total Points: 50

Answer each of the problems. Make sure to show all your work.

1. A commuter is driving along a highway on which the speed limit is 60 miles per hour when he

unknowingly runs into a speed trap involving two police officers. The first officer

mile marker 92 and clocks the commuter's car at 55 miles per hour. Five minutes police officer at mile marker 98 clocks the car at 60 miles per hour. Can the corn

with a speeding violation?

positioned at

later, a second

ester be charged

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2. A commuter is driving along a highway on whic the speed limit is 45 miles pier unknowingly runs into a speed trap involving two police officers. The first officer is mile marker 145 and clocks the commuter's'car at 45 miles per hour. Five minutes

ri- i cop? , hour when he • ' positioned at +1'1 e ‘t later; a second 1"16( V -C

police officer at mile marker 149 clocks the car at 40 miles per hour. Can the con charged with a speeding violation?

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Q {- 0 r.,\ e; , . (.9 (),,,1 ki, t 0 ()lid cg 3. Find the c value(s) that satin the !Clean ValUe Theorem for the function f (x) =

interval [-3, 2].

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4. Find the c value(s) that satisfy the Mean Value Theorem for the function f (x) =

the interval [1, 4]. 3I - 4x on

-1.

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1

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5. Find the c value(s) that satisfy the Mean Value Theorem for the function f (x) = 2x 2 + 5x + 2 on

the interval [-2, 0].

6. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x 3 + 2x2 + 1 on the

interval [-2, 0].

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7. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x 4 - 4x2 on the interval

[-3, 3].

8. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) =

—

1

x4

+ 2x3 1 1 +-

2 x + 6x - 5 on the interval [-5, 1].

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9. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x 3 - 2x 2 - 5x + 6 on

the interval [-2, 3].

10. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) =

x 4 + 5x 3 - 4x 2 - 44x - 48 on the interval [-4, 3].

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