problems-09-09-07

problems-09-09-07 - 8 that are tangent to f x = x 3(5 If f...

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Some Problems (1) Find the derivative of f ( x ). (a) f ( x ) = x ( x - 1) (b) f ( x ) = 1 + x 4 x 2 (c) f ( x ) = ax + b cx - d (d) f ( x ) = (3 x 2 - x ) ± 1 x + 3 ² (e) f ( x ) = 1 - t t 1 / 3 (2) Let p ( x ) = a n x n + a n - 1 x n - 1 + · · · + a 1 x + a 0 be a polynomial. Find p ± ( x ). (3) Suppose f (2) = - 3 , f ± (2) = - 2 , g (2) = 4 , g ± (2) = 7. Find h ± (2) for (a) h ( x ) = 5 f ( x ) - 4 g ( x ) (b) h ( x ) = 2 g ( x ) 1 + f ( x ) (4) Find two lines through the point (2
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Unformatted text preview: , 8) that are tangent to f ( x ) = x 3 . (5) If f, g, h are di±erentiable, what is ( f gh ) ± ( x )? (6) Calculate lim x → 1 x 2007-1 x-1 ....
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