test 2- 2007

# Test 2 2007 - graph models the catﬁsh population in the campus pond 7(8 pts Use the given information to sketch the graph of f Assume that f is

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Math 202-01 Exam 2 Spring 2007 Name: ID: Date: Directions: Show all work. No work equals no credit. You may use a basic scientiﬁc calculator, but no graphing calculators. Use proper notation. The test adds to 80 points and will be scaled to 100 points. 1. (8 pts) Given the demand (price) function p = 80 - q 4 , ﬁnd the revenue function, the maximum revenue (be sure to justify/check your answer), and the price that gives the maximum revenue. 2. (8 pts) Give the total cost function c = q 2 4 + 3 q + 400, ﬁnd the minimum average cost. Be sure to check your answer.

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3. (8 pts) Find the critical numbers (values), intervals of increasing and decreasing, and relative extrema of f ( x ) = 3 x 4 + 8 x 3 + 5. 4. (8 pts) Find the critical numbers (values), intervals of increasing and decreasing, and relative extrema of f ( x ) = x 4 / 3 - 4 x 1 / 3 where f 0 ( x ) = 4 x - 4 3 x 2 / 3 . 5. (8 pts) For f ( x ) = 3 x 5 - 5 x 4 + 2 x - 1 ﬁnd the intervals where it is concave up, concave down, and also any inﬂection points.
6. (4 pts) What is the signiﬁcance of the inﬂection point in the following ﬁgure. Assume that this

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Unformatted text preview: graph models the catﬁsh population in the campus pond. 7. (8 pts) Use the given information to sketch the graph of f . Assume that f is continuous on its domain and that all intercepts are included in the given information. Domain: R . Points: x-4-2 2 4 f ( x )-2-2 x-4-2 2 4 Sign Chart: f ( x ) – – – – – – – 0 + + + + ND– – – – 0 + + + + + + + f 00 ( x ) – – 0 + + + + + + + + + 0 + + + + + + + + + 0 – – 8. (20 pts) Diﬀerentiate the following functions. Do not simplify your answers. (a) s = ln[ t 3 ( t 2-1)] (b) y = 1 + ln x x 2 (c) y = 2 e ( x 2 +1) 3 (d) y = e 2 x 2 ln(4 x ) 9. (a) (8 pts) Find the elasticity of the demand function q = 49-2 p-p 2 when p = \$6. (b) How will a price increase aﬀect total revenue? Bonus: 5 points What is the formula that gives us the relationship between the change in revenue with respect to price and elasticity?...
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## This note was uploaded on 10/20/2010 for the course MATH 201 taught by Professor Smith during the Fall '08 term at Washington State University .

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Test 2 2007 - graph models the catﬁsh population in the campus pond 7(8 pts Use the given information to sketch the graph of f Assume that f is

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