Introductory Calculus: Test #1 Preparation
By M Ransom
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)?
Graph P(x) on the axes below using the WINDOW [0, 500] X [– 12000, 4000]. Label accurately and completely.
What happens to the profit when the number of items is increased from 311 to 312?
What is the average rate of change of profit between items 300 and 310?
What is the instantaneous rate of change of P(x) when x = 300? Explain what this number means.
Directions and/or Common Information:
Graph 
on the axes below. Label accurately.
on the axes below. Label accurately.
What is 
?
What is 
?
What is 
?
What is 
?
Discuss the continuity of at x = 1.
Directions and/or Common Information:
Calculate the derivatives of the following functions. (Simplify: NO negative exponents!)
Write an equation of the line tangent to 
at x = 2.