t3h.htm

Mathematics 2121-01
Calculus for Life Sciences I
Fall 03
Dr. A. Shlapentokh
Test #3

Compute the derivative:

(a)
(b)
(c)
(d)
(e)	None of the above

Compute the derivative:

(a)
(b)
(c)
(d)
(e)	None of the above

Compute the derivative:

(a)
(b)
(c)
(d)
(e)	None of the above

Suppose

and

are functions defined and differentiable everywhere. Suppose

. What is

(a)	0
(b)	3
(c)	4
(d)	2
(e)	None of the above

Compute the third derivative of

(a)
(b)
(c)
(d)
(e)	None of the above

Simplify

(a)	70
(b)
(c)
(d)
(e)	None of the above

Simplify

(a)
(b)
(c)
(d)
(e)	None of the above

Express the following in scientific notations:

(a)
(b)
(c)
(d)
(e)	None of the above

Express the following in scientific notations:

(a)
(b)
(c)
(d)
(e)	None of the above

10.

Compute:

(a)	1
(b)	2
(c)	3
(d)	4
(e)	None of the above

11.

Compute:

(a)	3
(b)	9
(c)
(d)	81
(e)	None of the above

12.

Compute:

(a)	1/2
(b)	3/4
(c)	4/5
(d)	0
(e)	None of the above

13.

Solve:

(a)
(b)
(c)
(d)	No solutions
(e)	None of the above

14.

Suppose

and

are related by the formula

, where

and

. What is the relationship between

and

(a)
(b)
(c)
(d)
(e)	None of the above

15.

Suppose

and

are related by the formula

, where

. What is the relationship between

and

(a)
(b)
(c)
(d)
(e)	None of the above

16.

Compute the derivative:

(a)
(b)
(c)
(d)
(e)	None of the above

17.

Compute the derivative:

(a)
(b)
(c)
(d)
(e)	None of the above

18.

Compute the derivative:

(a)
(b)
(c)
(d)
(e)	None of the above

19.

Compute the derivative:

(a)
(b)
(c)
(d)
(e)	None of the above

20.

Compute the derivative:

(a)
(b)
(c)
(d)
(e)	None of the above

21.

Compute the third derivative of

(a)
(b)
(c)
(d)
(e)	None of the above

22.

Compute the derivative:

(a)
(b)
(c)
(d)
(e)	None of the above

23.

Compute the derivative:

(a)
(b)
(c)
(d)
(e)	None of the above

24.

Compute the derivative:

(a)
(b)
(c)
(d)
(e)	None of the above

25.

Compute the derivative:

(a)
(b)
(c)
(d)
(e)	None of the above

26.

A certain population is growing exponentially at the annual rate of 3%. In 2000 the population was 50. Write down the formula for population

as a function of number of years

since 2000 in the form

(a)
(b)
(c)
(d)
(e)	None of the above

27.

A certain element is decaying exponentially and has a half life of 4 seconds. How long will it take it to loose 2/3 of its original amount ? (Round your answer to one tenth.)

(a)	Approximately 6.3 seconds
(b)	Approximately 2.6 seconds
(c)	Approximately 3.2 seconds
(d)	Approximately 2.3 seconds
(e)	None of the above

28.

If two non-negative numbers add up to 5, then the smallest possible sum of their cubes is

(a)	10.25
(b)	20.25
(c)	31.25
(d)	41.25
(e)	None of the above

29.

Find the largest value of the function

in the interval

(a)	4
(b)	-6
(c)	0
(d)	2
(e)	None of the above

30.

Find the maximum value of the function

in the interval

(a)	0
(b)
(c)	1
(d)
(e)	None of the above

31.

Determine the minimum value of the function

in the interval

(a)	no minimum value
(b)
(c)
(d)
(e)	None of the above

32.

Find all the critical points of the function

and determine their nature.

(a)	: local maximum, : local minimum, : local maximum
(b)	No critical points
(c)	: local maximum
(d)	: neither maximum, nor minimum, : local maximum
(e)	None of the above

33.

Find all the critical points of the function

and determine their nature.

(a)	: neither maximum, nor minimum
(b)	No critical points
(c)	: local maximum
(d)	: local minimum
(e)	None of the above

34.

Determine for what values of

the function

concaves up.

(a)	The graph never concaves up.
(b)	The graph always concaves up.
(c)	The graph concaves up for .
(d)	The graph concaves up for .
(e)	None of the above

35.

Find all the inflection points of the function

(a)
(b)
(c)
(d)
(e)	None of the above

(a)	The function is always increasing.
(b)	The function is always decreasing.
(c)	The function is increasing for and .
(d)	The function is increasing for
(e)	None of the above