1225FormA

8. A bowl of hot soup is set to cool. Let y = R ( t ) represent the rate at which the temperature of the soup is changing, in degrees Fahrenheit per minute, for a period of 10 minutes, 0 ≤ t ≤ 10. Values of R are given in the table below:

t (minutes) 0 3 8 10 R ( t ) ( ◦ F/minute) − 5 − 4 − 3 − 1

Assume that the temperature of the soup is 110 ◦ F at t = 0. Estimate the temperature of the soup at t = 10 minutes using L 3 , a Riemann sum with three sub-intervals whose sample points are left endpoints.

(A) − 36 ◦ F (B) − 41 ◦ F (C) 69 ◦ F (D) 74 ◦ F

9. The graph of y = f ( x ) is given below.

y

x

x 4

x 1

a

x 2 x 3

b

y = f ( x )

How many of the x -values labeled on the graph above ( x 1 , x 2 , x 3 , and x 4 ) satisfy the conclusion of the Mean Value Theorem for f on the interval [ a, b ]?

(A) 1

(B) 2

(C) 3

(D) 4

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