2. Sea \( f(x)=4 x^{2}-x+5 \) y \( g(x)=2 x^{3}-x \). Encuentra la derivada de \( h(x)=\frac{f(x)}{g(x)} \)

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.

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

s] Using calculus and showing all working, graph the function \[ f(x)=\frac{x+2}{x^{2}-1} \]

asymptotes of \( f \).

Decide whether the following statement is true or false. The cube function is odd and is increasing on the interval \( (-\infty, \infty) \). Choose the correct answer below. False True