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Unformatted text preview: Review Problems for the Final Exam Maxima, minima, convexity, concavity (a) Find all the critical points. (b) Use the second derivative test to determine if they are local maxima or local minima. Find the open intervals on which the function is (c) increasing, (d) convex. 1. f ( x ) = 2 3 x 3 x 2 4 x + 1 2. f ( x ) = 2 x + 18 x 3. f ( x ) = x x 2 +1 4. f ( x ) = 2 x 1 / 2 3 ln x + 4 √ x for x > 5. Find the critical points of f ( x ) = x ( x 1) 4 and use the first derivative test to determine if they are maxima or minima. 6. A ball is tossed straight up from an initial height of 15 meters. Suppose that the velocity is given by v ( t ) = 10 10 t meters/sec. (a) Determine the height h ( t ). (b) When does the ball reach its maximum height? What is the maximum height? (c) At what time does the ball hit the ground, i.e., h ( t ) = 0. MaxMin word problems. Remember to use the second derivative test....
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This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell.
 Spring '07
 DURRETT
 Calculus, Critical Point, Derivative

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