Question: : i. Find the domain of \(f\) and the asymptotes of the curve \(f\left( x \right)=\frac{{{x}^{2}}}{{{x}^{2}}-4}\)

ii. Compute and simplify \(f^{\prime}(x)\).

iii. Find the critical numbers of \(f\).

iv. Find the open intervals on which \(f\) is increasing and those on which it is decreasing

v. List the relative maxima and minima of \(f\). Also state where ( \(\mathrm{x}\) value) they occur.

vi. Compute and simplify \(f^{\prime \prime}(x)\).

vii. Find the \(x\) values where \(f^{\prime \prime}(x)=0\) or is undefined.

viii. Find the open intervals on which \(f\) is concave up and on which it is concave down.

ix. List the points of inflection. (Give both the \(x\) and \(f(x)\) values.)

x. Sketch the graph of \(f\) on the back or below.

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