Math 200 Practice Exam W/ Answers
Math 200 Practice Exam W/ Answers MATH 200
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This 10 page Study Guide was uploaded by Daija Randolph on Monday February 15, 2016. The Study Guide belongs to MATH 200 at Southeastern Louisiana University taught by Ken Li in Spring 2016. Since its upload, it has received 65 views. For similar materials see CALCULUS I in Applied Mathematics at Southeastern Louisiana University.
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Date Created: 02/15/16
MATH 20003 Practice Exam II 5 6 5 3 2 2 1. a. g(x) (2x 1) b. h(x) 2 tan (x ) c. u( y) y 4 y 5 d. v(t) 1 2t 1 t 2. Use implicit differentiation to find y . a. x xy y 33 b. y cos( xy) 2 3 3. Find the equation of the tangent line to the graph of x xy y 1 at the point (1,1) . 4. Sand falls from a conveyor belt at the rate of 10 cubic meter per minute onto the top of a conical pile, The height of the pile is always threeeighths of the base diameter. How fast are the (a) height and (b) radius changing when the pile is 4 meters high? 2 5. A particle moves along the parabola y x in the first quadrant in such a way that its x coordinate (measured in meters) increases at a steady rate 10 m/sec. How fast is the angle of inclination of the line joining the particle to the origin changing when x 3 m. 6. Find the maximum and minimum values of each function on the indicated intervals. a. f (x) x 27x 100 on [ 2,5] b. g(t) t 9 t 2 on [0,3] 7. Consider the function f (x) x 3 on the interval [1,3 ] , find all the values of c in [1,3 ] such that f '(c) f (b) f (a) . b a 8. Determine where the function is increasing and where is decreasing 3 2 2 / 3 a. f (x) x 6x 25 b. g(x) (x 4) 1 9. Find all relative extrema of each function 2 2 2 / 3 a. f (x) (x 2) (x 1) b. g(x) (x 9) 10. State true or false for each statement. If it is false, explain why or give an example that shows it false. a. Every nthdegree polynomial has (n1) critical numbers f (c) b. If c is a critical number of the function f, then is a relative maximum or minimum of the function c. f is a cubic polynomial whose graph has three xintercepts, then its graph has two horizontal tangent lines d. If f is a continuous even function, then f '(0) 0 11. Find the points of inflection and use the second derivative test to find all relative extrema for the function f (x) 2x (1 x ) 2 .
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