Question: Let: f left parenthesis x right parenthesis equals x over open parentheses x minus 1 close parentheses squared comma space space f to the power

Let: f left parenthesis x right parenthesis equals x over open parentheses x minus 1 close parentheses squared comma space space f to the power of apostrophe left parenthesis x right parenthesis space equals space minus fraction numerator open parentheses x plus 1 close parentheses over denominator open parentheses x minus 1 close parentheses cubed end fraction comma space space space f to the power of apostrophe apostrophe end exponent left parenthesis x right parenthesis equals fraction numerator 2 x plus 4 over denominator open parentheses x minus 1 close parentheses to the power of 4 end fraction

Find x− and y− intercepts of the graph of f, if it has any.

Find vertical and horizontal asymptote(s) of f, if it has any.

Find the critical number(s), intervals(s) of increasing and decreasing and points of relative extrema of f, if it has any.

Find intervals of concavity and the point(s) of inflection of f, if any.

Sketch the graph of f, label all important points from part (1), (2) and (3).

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