guide2h.htm

Mathematics 2121-003
Calculus for Life Sciences I
Spring 05
Dr. A. Shlapentokh
Study Guide #2

Find the rate of change between

(a)
(b)
(c)

Suppose the average rate of change of

Suppose the average rate of change of

for any function

differentiable at

for some real number

. Is there a value of

which will make this function continuous at

for some real number

. Is there a value of

which will make this function continuous at

Is the function

? Does this function have a derivative at

does the following equality hold for any function differentiable at

Compute the derivative of

using the definition of the derivative.

Compute the derivative of

using the definition of the derivative.

Compute the derivative of

using the definition of the derivative.

What is the slope of the tangent line to the graph of the function

What is the equation of the tangent line to the graph of

Suppose the amount of some chemical in the blood of a patient is described by the formula

is measured in minutes and

is measured in mg. Find the instantaneous rate of growth of the amount of the chemical at

Differentiate, using the product rule,

Using the same information as in the preceding problem, compute

are functions defined and differentiable everywhere. Suppose

Compute the third derivative of

Compute the second derivative of

Express the following in scientific notations:

Express the following in scientific notations:

Express the following in scientific notations:

are related by the formula

. What is the relationship between

are related by the formula

. What is the relationship between

Compute the derivative:

Compute the derivative:

Compute the derivative:

Compute the derivative:

Compute the derivative:

Compute the derivative:

Compute the derivative:

Compute the third derivative of

Compute the derivative:

Compute the derivative:

Compute the derivative:

Compute the derivative:

Compute the derivative:

Compute the third derivative of

A certain population is growing at annual rate of 3% compounded continuously. In 1998 the population was 500. What will it be in 2005?

Consider the same population as in the problem above but use once a year compounding. Assume again that the population size was 500 in 1998 and determine the population in 2005.

Suppose a certain radioactive element is decaying exponentially with a half time equal to 1000 years. How long will it take for 75% of the original amount to be lost?

Determine for what values of

Find all the inflection points of the function

For what values of

is the function

For what values of

is the function

For what values of

is the function

For what values of

is the function

Amongst the graphs below which graph(s) has (have) an inflection point ?