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Introductory Calculus: Test #1 Preparation
Question Group #1
Directions and/or Common Information:
The fixed weekly cost for manufacturing a commodity is $1,000. The
variable
cost for manufacturing x items is given by V(x) =
and the revenue is given by R(x) =
.
The profit P(x) is given by revenue minus cost or R(x) – (V(x) + 1000).
What is the profit
function
P(x)?
1.
Graph
P(x) on the axes below using the WINDOW [0, 500] X [– 12000, 4000]. Label accurately and completely.
2.
What happens to the profit when the number of items is increased from 311 to 312?
3.
What is the average
rate
of change of profit between items 300 and 310?
4.
What is the instantaneous
rate
of change of P(x) when x = 300?
Explain
what this number means.
5.
Question Group #2
Directions and/or Common Information:
Graph
on the axes below. Label accurately.
1.
What is
?
2.
What is
?
3.
What is
?
4.
What is
?
5.
Discuss the continuity of
at
x
= 1.
6.
Question Group #3
Directions and/or Common Information:
Calculate the derivatives of the following functions. (Simplify: NO negative exponents!)
1.
2.
3.
Write an
equation
of the
line
tangent to
at x = 2.
4.
M Ransom
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