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test 2- 2006 - 12 x 6 is increasing or decreasing and find...

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Math 202-01 Exam 2 Spring 2006 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 use of pen will also result in a score of zero. 1. (25 pts) Find the derivatives of the following. Do not simplify your answers. (a) y = ln(3 x 2 + 2 x + 1) (b) f ( z ) = ln z z (c) y = ln h (5 x + 2) 4 (8 x - 3) 6 i (d) y = e x 2 +6 x +1 (e) y = ( e 2 x + 1) 3
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2. (8 pts) Find the point of elasticity of the demand equation q = 100 - p when p = 50 and determine whether demand is elastic, is inelastic, or has unit elasticity. 3. (10 pts) Use implicit differentiation to find dy/dx when x 2 + y 2 = 2 xy + 3. 4. (10 pts) Use logarithmic differentiation to find y 0 when y = (3 x + 4)(8 x - 1)(3 x 2 + 1) 4 .
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5. (8 pts) Given y = 1 2 x + 3 , find d 2 y dx 2 . 6. (9 pts) Find where y = - x 3 + 6 x 2 -
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Unformatted text preview: 12 x + 6 is increasing or decreasing and find where the relative maxima and minima occur. 7. (10 pts) Find where y =-x 4 4 + 9 x 2 2 + 2 x is concave up or concave down and find the x-values where the inflection points are. 8. (8 pts) Find all asymptotes of f ( x ) = 2 x 2 x 2 + x-6 . 9. (12 pts) For a monopolist’s product, the demand equation is p = 40 √ q and the average-cost function is c = 1 3 + 2000 q . Find the profit-maximizing price and output. At this level, show that marginal revenue is equal to marginal cost. Extra Credit 5 pts State the relationship between elasticity and marginal revenue. Hint: Differentiate r = pq ....
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