\begin{tabular}{l|l} Ermitteln Sie die Steigung der Tangente des Graphen der Funktion \\ \( f(x)=-2 x^{3}+x^{2}+4 x-1 \) im Punkt \( P(2 \mid-5) \). \\ Geben Sie den Wert auf zwei Nachkommastellen gerundet ein. \end{tabular}

Find the derivative of the following function. \[ f(x)=\frac{x^{3}-9 x^{2}+x}{x-1} \]

Calcular el área de las siguientes regiones que están delimitadas por las siguientes curvas cuyas ecuaciones son: A) \( \mathrm{y}=\mathrm{x}+6 \quad ; \quad \mathrm{y}=\mathrm{x}^{3} \quad ; 2 \mathrm{y}+\mathrm{x}=0 \)

Calculate the limit. \[ \lim _{h \rightarrow 0} \frac{4(3+h)^{2}-36}{h}=\square \text { (Simplify your answer.) } \]

Determine the intervals on which the following function is continuous. \( f(x)=\frac{x-10}{x^{2}-100} \)

A. ctangle initially has dimensions 2 cm by 7 cm . All sides begin increasing in length at a rate of \( 2 \mathrm{~cm} / \mathrm{s} \). At what rate is the area of the rectangle increasing after 16 s ? Let \( \mathrm{A}, \mathrm{b} \), and h be the area, base, and height of a rectangle, respectively. Write an equation relating \( \mathrm{A}, \mathrm{b} \), and h . \( \mathrm{A}=\mathrm{b} \times \mathrm{h} \) Differentiate both sides of the equation with respect to t . \( \mathrm{dA}= \)