Ap English Essay

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Cuyamaca College Math 180 Name:________________________ Instructor: Dan Curtis Practice Exam 3 1. Car A is travelling west toward an intersection at 40 mph. Car B is travelling north toward the same intersection at 60 mph. At what rate are the cars approaching each other when car A is 3 miles from the intersection and car B is 4 miles from the intersection? 2. A spherical balloon is being filled with water at the rate of 100 cm3 per second. At what rate is the radius increasing when the radius is 15 cm? 4. Find the critical values of the following functions. a) f ( x) 3x 4 4 x3 6 x 2 b) y p 1 p2 4 5. Find the absolute maximum and minimum values of f on the given interval. [ 1, 2] a) f ( x) ( x 2 1)3 , b) f (t ) t ln t , [ 1 , 2] 2 6. Verify that the function satisfies the conditions of the Mean Value Theorem, and then find all numbers c that satisfy the conclusion of the Mean Value Theorem. f ( x) x3 x 1, [0, 2] 7. Use Rolle’s Theorem to show that the equation 1 2 x x3 4 x5 0 has exactly one real solution. 8. Let f ( x) x2 x2 9 . a) Find the domain of f. b) Find the x and y intercepts. c) Find any symmetries of f. d) Find the vertical and horizontal asymptotes. e) Find intervals of increasing and decreasing. f) Find all local maximums and minimums. g) Find all intervals of concavity and inflection points. h) Sketch the curve. 9. Find the point on the line y 4 x 7 that is closest to the origin. 10. The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P 100 x x x 4 2 where x is the light intensity (measured in thousands of foot candles). For what light intensity is P a maximum?

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