(Solved): 4. Sketch the graph of a function that satisfies all the given conditions ( 1 ...

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4. Sketch the graph of a function that satisfies all the given conditions ( 10 marks) \[ \begin{aligned} f(1)=f^{\prime}(1)=0, & \lim _{x \rightarrow 2^{+}} f(x)=\infty, \quad \lim _{x \rightarrow 2^{-}} f(x)=-\infty \\ \lim _{x \rightarrow 0} f(x)=-\infty, & \lim _{x \rightarrow-\infty} f(x)=\infty, \quad \lim _{x \rightarrow \infty} f(x)=0 \\ f^{\prime \prime}(x)>0 \text { for } x>2, & f^{\prime \prime}(x)<0 \text { for } x<0 \text { and } f \text { or } 00 \) for \( x>2, \quad f^{\prime \prime}(x)<0 \) for \( x<0 \) and for \( 0