calculus-1-asignment-6 (1).pdf - Jacobs University Bremen...

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Jacobs University Bremen Fall Semester 2017 Prof. Dr. T. Preusser Calculus I Assignment Sheet 6. Due: Oct 18, 2017 Problem 16 [10 Points]: Compute the derivatives of the following functions: a) a ( y ) = ( y 3 - p y ) ( y 2 + 2 p y ) b) b ( u ) = ( u 2 + 1) 3 ( u 2 - 1) 2 p u - 2 c) c ( x ) = r x + q 1 + p x For the following functions find the equation of the tangent line at the specified points P = ( x 0 , f ( x 0 )), i.e. the line whose slope is given by the derivative f 0 ( x 0 ) and which passes through P : d) f ( x ) = 4 x ( x 5 + 1) , P = (1 , 8) e) f ( x ) = t 2 1 + p t , P = 4 , 16 3
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