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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