Chapter 4 Test

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Name:

Chapter 4 Test

Multiple Choice

Identify the letter of the choice that best completes the statement or answers the question.

For an object moving in a straight line,

a.	the position function is the derivative of the velocity function
b.	the velocity function is the derivative of the position function
c.	sometimes a) is true, and sometimes b) is true, depending on the situation
d.	neither a) nor b) is true in all cases

The derivative of a function

evaluated at

a.	the slope of the tangent to the graph of f at
b.	the instantaneous rate of change of f at
c.	the limit of the slopes of secants to the graph of f over the intervals between and as h approaches 0
d.	all of the above

A standard notation for the derivative of the function y = f (x) is

a.	c.
b.	d.	all of the above

State which function is not differentiable at

a.		c.
b.		d.

The derivative of the function

a.		c.
b.		d.

, and

is equal to

a.	c.	0
b.	d.

For an object moving in a straight line, if the velocity and acceleration have opposite signs, the object is

a.	speeding up	c.	moving away from the origin
b.	slowing down	d.	moving toward the origin

Problem

The population of a city t years from now is modelled by chapter_4_files/i0100000.jpg

, where P is measured in millions.

a) Determine the current population.

b) Determine a formula for

c) Determine

d) Explain the meaning of

A stone is dropped into a mine shaft.

a) If the stone hits the bottom of the mine shaft after 10 s, how deep is the shaft?

b) What is the velocity of the stone when it reaches the bottom of the shaft?

10.

a) If the profit function has a maximum, what is the value of the marginal profit when the profit is at its maximum?

b) What is the relation between marginal cost and marginal revenue when profit is at the maximum?