\begin{tabular}{l} Question \\ Consider the function \( f(x) \) below. Over what open interval(s) is the function decreasing and concave up? Give your answer \\ in interval notation. \\ \( \qquad f(x)=\frac{x^{4}}{4}-\frac{75 x^{2}}{2}-250 x-4 \) \\ Enter \( \varnothing \) if the interval does not exist. \\ Provide your answer below: \\ \hline\end{tabular}

Proporre un esempio di funzione \( g(x) \) tale che \[ \lim _{x \rightarrow+\infty} \frac{g(x)}{3 \log ^{2} x+1}=+\infty \]

5. [12 marks] Using calculus and showing all your working, sketch the function \[ f(x)=\frac{x}{x^{2}-4} \] noting the domain of \( f(x) \), any intercepts or asymptotes, symmetry, regions where the function is increasing or decreasing and any relative extrema. Note: You don't have to consider the second derivative and concavity.

\( \lim _ { n \rightarrow + \infty } \frac { n ^ { 5 } + \sin n } { 3 ( \arctan n ) n ^ { 5 } } \)

Gegeben ist eine weitere Funktion h. mit der Gleichung \( h(x)=0,5 x^{3}-4 x^{2}+6 x+2 \) 74 a) Untersuchen Sie den Graphen von \( h \) auf mögliche Wendepunkte.

asymptotes of \( f \).