INSTRUCTOR: JOS ´ E MANUEL G ´ OMEZ Homework 8. Due date Wednesday November 2, 2011 Please show all your work. (1) (5 Points) Consider the function f ( x ) = √ 2 x + 2. Use a suitable the linear approxi-mation on the function f ( x ) to estimate √ 4 . 2. (2) (10 Points) Suppose that w ( x ) = x 2 x 2 + 1 . Find the intervals where w ( x ) is increasing, decreasing, concave up and concave down. (3) (10 Points) Consider the function g ( x ) = xe − 2 x 2 . (a) Find where the function g ( x ) is increasing and where it is decreasing. (b) Find where the function g ( x ) is concave up and where it is concave down. (c) Find the points on the graph of g ( x ) where it has a local maximum and where it has a local minimum. (d) Find the in±ection points on the graph of g ( x ). (4) (5 Points) Sketch the graph of a function h ( x ) de²ned on the interval (0 , 3] such that • h ( x ) does not have an absolute maximum on the interval (0 , 3].
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