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(1 pt) Suppose that an object moves along the y-axis sot hat its location

is y = x x is in seconds.)

+8x at time x. (Here y is in meters and

(A) Find the average velocity (the average rate of change of y with respect to x) for x changing from 2 to 9 seconds (include units).

Average velocity =

(B) Find the average velocity for x changing from 5 to 5 + h seconds.

Average velocity =

Instantaneous velocity =

Answer(s) submitted:

• 19 m/s
•

• 18 m/s

(score 0.6666666865348816)

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2 The cost (in dollars) of producing x units of a certain commodity is

C(x) = 6500 + 19x + 0.2x2.

(a) Find the average rate of change of C with respect to x when the production level is changed

(i) from x = 100 to x = 105. Average rate of change =
(ii) from x = 100 to x = 101. Average rate of change =

(b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.)

Instantaneous rate of change =

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4. (1 pt)

Let f (x) = x3 − 2x. Calculate the difference quotient f(3+h)−f(3) for

h h=.1

h=.01
h=−.01
h=−.1
If someone now told you that the derivative (slope of the tangent line to the graph) of f (x) at x = 3 was an integer, what would you expect it to be?

Answer(s) submitted:

• • • • •

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5. (1 pt)

Let f (x) = 1 . Calculate the difference quotient x−4

f(−1+h)−f(−1) for h

h=.1
h=.01
h=−.01
h=−.1
If someone now told you that the derivative (slope of the tangent line to the graph) of f (x) at x = −1 was −1/n2 for some integer n what would you expect n to be?

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6. (1 pt) √

Let f (x) = x + 5. Calculate the difference quotient f(11+h)−f(11) for

h h=.1

h=.01

h=−.01
h=−.1
If someone now told you that the derivative (slope of the tangent line to the graph) of f (x) at x = 11 was 1/n for some integer n whatwouldyouexpectntobe?
n=