Practice Quiz 3a

Practice Quiz 3a - x = 10 4 . Let ( x ) be the function so...

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Practice Test Test IIIA for Calculus I I Consider the function f ( x )=(1 - sin( x )) sin( x )0 x 2 π. (a) Find all of the zeros of this function,i.e., all solutions of f ( x )=0. (b) Find values of x for which f 0 ( x ) = 0 (In other words, all of the critical numbers ). (c) Find all of the maxima and all the minima. II Let a and b be any two positive numbers such that ab = 1. How small can a 2 + b be? Find the values of a and b that make it as small as possible. III Consider the function f ( x )= xe 2 x Find a function F ( x )sothat F 0 ( x )= f ( x ) for all x and so that F 0 (0) = F (0). IV (a) Let f ( x )= x 1 / 4 and let x
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Unformatted text preview: x = 10 4 . Let ( x ) be the function so that y = ( x ) is the tangnet line to y = f ( c ) at x . Find the numbers a and b so that ( x ) = ax + b . (b) Evaluate (10 , 010) and using the second derivative of f , nd a number c so that (10 , 010) 1 / 4 = (10 , 010) c . V Let f ( x ) = x 3 ( x-1) 2 . (a) Find all the asymptotes, if any. (b) Sketch the graph showing all the asymptotes. (You need not sketch f itself)....
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