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Solve the Problem x>0x > 0 , Sketch a Curve y=f(x)y = f ( x )

Question 5

Essay

Solve the problem.
-For x>0x > 0 , sketch a curve y=f(x)y = f ( x ) that has f(1)=0f ( 1 ) = 0 and f′(x)=−1xf ^ { \prime } ( x ) = - \frac { 1 } { x } . Can anything be said about the concavity of such a curve? Give reasons for your answer.

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