16AHW3 - we have a relative minimum and f(1 = 0 So 0 si a...

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Math 16A, Spring 2010 HW3, May-21-10 Due by May-28-10. I will collect HW3 in class We will grade randomly one of the following exercises: 1. Calculate the second derivative of the following functiuons example f ( x ) = 2 x 3 + 4 x 2 f 0 ( x ) = 6 x 2 + 8 x differentiating again we get f 00 ( x ) = 12 + 8 A f ( x ) = (2 x 2 + x ) sin ( x ) B f ( x ) = x tan ( x ) C f ( x ) = x 2 +1 x +2 D f ( x ) = x + 2 cos ( x ) E f ( x ) = ( x 3 + 2 x ) p sin ( x ) 2. Find the critical number x = c and the intervals in which the function is increasing or decreasing. Evaluate f ( x ) in the critical points and sketch the graph of the function. example f ( x ) = x 2 - 2 x f 0 ( x ) = 2 x - 2 so f(x) is differentiable everywhere and we get f 0 ( x ) = 2( x - 1) = 0 x = 1 so x = 1 is the only critical point. f ( x ) is decreasing before 1 (TEST f 0 (0) = - 2) and increasing after 0 (TEST f 0 (2) = 2) moreover f (1) = - 1 1
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A f ( x ) = x x + 1 B f ( x ) = x 2 x 2 +4 C f ( x ) = sin ( x ) - cos ( x ) D f ( x ) = | x 2 - 4 | E f ( x ) = ( 4 - x 2 when x 0 - 2 x when x > 0 3. Find the relative extrema of the following fcts example f ( x ) = | x - 1 | That fct is not differentiable in x = 1. There
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Unformatted text preview: we have a relative minimum and f (1) = 0. So 0 si a relative min and occurs for x = 1 A f ( x ) = ( x-1) 3 B f ( x ) = ( x-1) 2 3 C f ( x ) = √ x 2-1 D f ( x ) = sin 2 ( x ) E f ( x ) = x x +1 4. Find the absolute extrema of the following fcts in the given interval example f ( x ) = x 2 [-1 , 3]. We need to look for abs extrema in the critical point and on the boundary. f ( x ) = 2 x = 0 → x = 0 and we have f (0) = 0. On the boundary f (-1) = 1 and f (3) = 9. So 9 is the abs max occurring in x = 3 while the abs min is 0 and occurs in x = 0 A f ( x ) = | x 2-4 | [-4 , 5] B f ( x ) = ( x-5) 2 / 3 [2 , 7] C f ( x ) = x 2 x 2 +3 [-1 , 1] D f ( x ) = ( x-1) 2 3 [-5 , 2] E f ( x ) = cos ( x ) sin ( x ) [0 ,π ] 2...
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This note was uploaded on 10/08/2010 for the course MATH 16A taught by Professor Sabalka during the Spring '08 term at UC Davis.

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16AHW3 - we have a relative minimum and f(1 = 0 So 0 si a...

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