Suppose That F Is a Continuous Function And $f ( 0 ) = 0 , f ( 2 ) = f ( - 2 ) = 1 , f ^ { \prime } ( 0 ) = 0 , f ^ { \prime } ( x ) > 0$

question 199

Essay

Suppose that f is a continuous function and $f ( 0 ) = 0 , f ( 2 ) = f ( - 2 ) = 1 , f ^ { \prime } ( 0 ) = 0 , f ^ { \prime } ( x ) > 0$ for $x > 0 , f ^ { \prime } ( x ) < 0$ for $x < 0 , f ^ { \prime \prime } ( x ) > 0$ for $| x | < 2 , f ^ { \prime \prime } ( x ) < 0$ for $| x | > 2$ , and $\lim _ { x \rightarrow \infty } f ( x ) = \lim _ { x \rightarrow - \infty } f ( x ) = 2$ . Sketch the graph of $y = f ( x )$ .

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