Show all
work on separate paper. Turn in ALL worksheets. Give all irrational
answers in exact (radical) form. When you use the calculator, say so, and
explain what you did.
1. Find the maximum and minimum values of the function (if they
exist):
a)
on
[-1, 2].
b)
on
(0, 2).
c)
on [1, 4).
2. Find the values of c for which the Mean Value Theorem applies, or
explain why the theorem does not apply.
a)
on
[-1, 1].
b)
on [0, 6].
3. Evaluate the limits:
a)
b)
c)
d)
e)
f)
4.
Given 
,
use the first derivative test to find all critical values, identify x
coordinates of relative maximum and minimum points, and give intervals
in which the graph is increasing and decreasing.
5. Given 
,
,
,
find the x-coordinates of all points of inflection. Give
intervals in which the graph is concave up and concave down. What
conditions are necessary to have a point of inflection?
In 6-7,
sketch the graphs, find x and y intercepts, horizontal and vertical
tangents, vertical asymptotes, and
and
.
Describe your window.
6. Sketch the graph of
7. Sketch the graph of .
8.
Given 
,
set up a formula to find the root by Newton’s Method. Beginning with
x=1, draw a sketch (or an outline of steps) to illustrate how Newton’s
Method works, and give a list of x values leading to the root.
If you used a calculator method or program, describe what you did.
9. Given
,
find ∆f and df when x = 5 and ∆x = dx=
0.1.
10. A farmer
plans to fence a rectangular garden adjacent to a river. The garden
must contain 1250 square feet. What dimensions would require the least
amount of fencing if no fence is required along the river. How many
feet of fence are needed?
11. Equal
squares are to be cut from each corner of a piece of tin measuring 6
meters by 6 meters, and the edges are then turned up to form a box with
no lid. What are the dimensions of the box with maximum volume, and
what is the volume of the box?
Return to Calculus I Practice Tests
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