241finf - Calculus I (Math 241) Final Problem 1. [16...

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Calculus I (Math 241) – Final Problem 1. [16 Points] Calculate the derivatives of the following functions: f ( x ) = sec( x 2 +1) , g ( x ) = r tan(2 x ) , h ( x ) = sin(2 x ) x 3 - 1 , t ( x ) = cos p 1 + x 1 - x P . Problem 2. [16 Points] Calculate the integrals: i x x - 1 dx, i cos x sin 7 x dx, i dt 4 - x 2 , i 2 1 | x | dx. Problem 3. [20 Points] Discuss the function f ( x ) = x ( x - 1) 2 ( x - 2) = x 4 - 4 x 3 + 5 x 2 - 2 x. SpeciFcally, address the following: 1. ±ind the intercepts and the intervals on which the function is positive or negative, respectively. 2. ±ind the critical points and the intervals on which the function is in- creasing, resp., decreasing. 3. ±ind the intervals on which the function is concave up, resp., concave down. 4. ±ind the local maxima and minima and the in²ection points. 5. Sketch the graph in accordance with the information obtained above. Problem 4. [14 Points] Use Frst principles to Fnd f ( a ) if f ( x ) = x .
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241finf - Calculus I (Math 241) Final Problem 1. [16...

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