Solve the Problem $\mathrm { f } ^ { \prime } ( \mathrm { x } ) > 0$

question 38

Essay

Solve the problem.
-Sketch a smooth curve through the origin with the following properties: $\mathrm { f } ^ { \prime } ( \mathrm { x } ) > 0$ for $\mathrm { x } < 0 ; \mathrm { f } ^ { \prime } ( \mathrm { x } ) < 0$ for $\mathrm { x } > 0$ ; $\mathrm { f } ^ { \prime \prime } ( \mathrm { x } )$ approaches 0 as $x$ approaches $- \infty$ ; and $f ^ { \prime \prime } ( x )$ approaches 0 as $x$ approaches $\infty$ .

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