Test 1Bridges Name ____________________Math 115B Feb 24, 2004Test 1(Pencil and Paper)1. Let 48183)(2 xxxf. Calculate ]5,1[,3fS. YOU MUST SHOW ALL WORK IN A CLEAR AND ORGANIZED MANNER. FAILURE TO DO SO WILL RESULT IN REDUCED OR NO POINTS. 2. A company has determined that the demand function for a commodity it wants to produce is given by 8000003125.0)(2 qqD and that the cost function to produce it is.1950270)( qqC(a) Calculate the intercept on the D(q)-axis. What does this result mean? BE SURE TO SHOW HOW YOU DETERMINED THIS – AN ANSWER BASED ON A GRAPH IS NOT ACCEPTABLE.(b) Calculate the intercept on the q-axis. What does this result mean? BE SURE TO SHOW ALL WORK – AN ANSWER BASED ON A GRAPH IS NOT ACCEPTABLE.(c) Calculate the profit the company would make from a sale of 1000 items. SHOW ALL WORK AND GIVE ANSWER TO 2 DECIMAL PLACES. A SOLUTION BASED ON A GRAPH IS NOT ACCEPTABLE.3. Consider 975)(2 xxxg.1(a) Find the slope of the tangent line to )(xg at x = – 2. SHOW ALL WORK AND GIVE EXACT ANSWER.(b) Use algebra to find the equation of this tangent line at x = – 2. SHOW ALL WORK AND GIVE EXACT ANSWER.4. Another company finds that its demand function is 120048.0)( qqD and that the cost function is .2003.0)( qqC(a) Find the equation of the profit function in simplest form.(b) Find the equation of the marginal cost function in simplest form.(c) Find the equation of the marginal profit function in simplest form.(d) Calculate the value of q that gives the maximum profit. SHOW ALL WORK AND GIVE ANSWER TO 2 DECIMAL PLACES. A SOLUTION BASED ON A GRAPH IS NOT ACCEPTABLE.5. Let xxk 6.2)( . Use the definition of the derivative and h = 0.001 to calculate )7(k.2ROUND FINAL ANSWER TO 4 DECIMAL PLACES. DO NOT ROUND YOUR NUMBERS UNTIL THE VERY END OF THE PROBLEM. YOU MUST SHOW ALL WORK IN A CLEAR AND ORGANIZED MANNER. FAILURE TO DO SO WILLRESULT IN REDUCED OR NO POINTS. 6. The graph of a demand function is given below.Demand Function-2502550750 25000 50000 75000QuantityUnit Price(a) Compute the total possible revenue. SHOW ALL WORK.(b) Compute the revenue when q = 30,000. SHOW ALL WORK.(c) Compute the consumer surplus when q = 30,000. SHOW ALL
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