finalguideh.htm

Mathematics 2121-001
Calculus for Life Sciences I
Fall 03
Dr. A. Shlapentokh
Final Guide

Find the increment of the function

in the interval

. Find the corresponding

Find the average rate of change for the function

in the interval

. Find the average rate of change of

in the interval

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

A population of a certain bacteria grows according to the formula

is measured in hours and

is measured in mg. Find the average rate of growth of the population of the bacteria between t=2 and t=4 hours.

Find two non-negative numbers whose sum is 10 and the product is as small as possible.

A farmer is making a rectangular yard using 500 ft of fencing. How big can the area of the yard be?

Find the largest value of the function

in the interval

Find the absolute minimum and maximum values of

in the interval

Determine the minimum value of the function

in the interval

Determine the maximum value of the function

in the interval

Determine the minimum value of the function

in the interval

Determine the minimum value of the function

in the interval

Determine the minimum value of the function

in the interval

Find all the critical points of the function

and determine their nature.

Find all the critical points of the function

and determine their nature.

Find all the critical points and determine their nature for the function

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

What is the 100-th derivative of

What is the second derivative of

A certain population is growing at the uniform rate of 3% a year. In 1998 the population was 500. Write down the formula for population

as a function of number of years

since 1998 in the form

A certain element is decaying exponentially and has a half life of 5 seconds. How long will it take it to loose 1/3 of its original amount?

After 5 years of growing at the rate of 5% a population reached 10,000. What was the initial population?

Compute the derivative of

Compute the derivative of

Compute the derivative of

Compute the derivative of

Compute the derivative of

Compute the derivative of

Compute the derivative of

Compute the derivative of

Compute the derivative of

Compute the derivative of

Compute the derivative of

Compute the derivative of

using scientific notations.

is a function differentiable everywhere. What value of

will make the following equality true:

. What is the formula for

. For what value of

is this function continuous at

. For what value of

is this function continuous at

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

Amongst the graphs above which graph(s) has (have) a critical point?

Amongst the graphs below which one corresponds to the function

Amongst the graphs below which one corresponds to the function

Amongst the graphs below which one corresponds to the function

Amongst the graphs below which one corresponds to the function

Suppose two functions differentiable everywhere are related by the equation

Suppose you are inflating a balloon. Assume that at

hours its radius is changing at the rate of

inches/hour. Assume also that at

inches. What is

Two trucks leave a depot at the same time. One is going north, the other is going west. 5 hours after the departure the speed of the first truck is

mph, the speed of the second truck is

mph. The first truck is 200 miles away from depot and the second truck is 100 miles away from the depot. How fast is the distance between the trucks changing 4 hours after the departure?

A scientist is studying the change in values of two variables

over time. She has determined that the variables satisfy the following equation

is a constant. During the latest measurement it was established that

is time. Determine the value of

during the latest measurement.

Find all the critical points of the following functions and use the first derivative test to determine their nature.

(a)
(b)
(c)
(d)
(e)