241find - Calculus I(Math 241 Final Problem 1[16 Points...

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Calculus I (Math 241) – Final Problem 1. [16 Points] Calculate the derivatives of the following functions: f ( x ) = tan 2 x, g ( x ) = r 1 + cos(2 x ) , h ( x ) = 5 x sec( x 2 ) , t ( x ) = 1 1 + x 2 . Problem 2. [16 Points] Calculate the integrals: i π 3 0 cos(2 x ) dx, i x 2 x + 2 dx, i dt 4 - t 2 , i π 3 0 cos 2 x dx. Problem 3. [25 Points] Discuss the function f ( x ) = ( x - 2)( x + 1) 2 = x 3 - 3 x - 2 . SpeciFcally, address the following: 1. ±ind the intercepts and the intervals on which the function is positive, resp., negative. 2. ±ind the critical points and the intervals on which the function is in- creasing, resp., decreasing. 3. ±ind the in²ection points and the intervals on which the function is concave up, resp., concave down. 4. ±ind the local maxima and minima. 5. ±ind the absolute extrema of the function on the interval [ - 1 . 3 , 3]. 6. Sketch the graph in accordance with the information obtained above.
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This note was uploaded on 07/26/2009 for the course MATH 215 taught by Professor Heiner during the Spring '09 term at Hawaii.

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241find - Calculus I(Math 241 Final Problem 1[16 Points...

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