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 )

Question

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 $y = f ( x )$ .

Quizplus · Accepted Answer

The Answer of 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 $y = f ( x )$ .

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

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