t1(2) - (b) What is the height after 2 seconds? (c) What is...

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Methods of Calculus MAC3233 Test 1 June 5, 1995 Instructions: Do not write your answers on this paper, use separate answer sheets. This is a closed- book test. No calculators are allowed to be used. To receive credit, you must show all work. You are not required to simplify your answers. 1. (10 pts.) If f ( x ) = x , compute f (9) and f 0 (9). Find the equation of the tangent line to the graph of y = f ( x ) at the point where x = 9. 2. (5 pts.) Find dy dx , if y = x - 1 3 . 3. (10 pts. each) Differentiate: (a) f ( x ) = 3 x + 2 x - 1 (b) f ( x ) = 14 ( 1 + 2 x - x 5 ) 9 (c) f ( x ) = 8 x 2 + 2 x - 1 4. (10 pts.) Suppose the revenue from producing (and selling) x units of a product is given by R ( x ) = . 01 x 2 - 3 x dollars. Find the marginal revenue at a production level of 1800. 5. (10 pts.) A ball is thrown upward. Let s ( t ) be the height of the ball, in feet, after t seconds. Suppose that s ( t ) = 5 + 128 t - 16 t 2 . (a) What is the velocity after 2 seconds?
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Unformatted text preview: (b) What is the height after 2 seconds? (c) What is the acceleration after 2 seconds? (d) Is the ball rising or falling, after 2 seconds? 6. (10 pts.) Use the following information to make a good sketch of the function f ( x ) near x = 3: f (3) = 4, f (3) =-2 3 , f 00 (3) = 5. 7. (15 pts.) Let y = 1 2 x 3 + 3 2 x 2-12 x-13. (a) Find y ( x ) and y 00 ( x ). (b) Find all relative extreme points and indicate whether each is a relative maximum or minimum. (c) Find all inection points. (d) Plot the points found in steps (b) and (c) above. Sketch the graph. 8. (10 pts.) The graph of y = f ( x ) is shown below. Explain why f ( x ) must have a relative minimum point at x = 3.-9 -6 -3 3 6 9 x y y = f ( x )...
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