A company manufactures and sells \( x \) television sets per month. The monthly cost and price-demand equations are \( C(x)=73,000+80 x \) and \( p(x)=200-\frac{x}{30}, 0 \leq x \leq 6000 \). (A) Find the maximum revenue. (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. (C) If the government decides to tax the company \( \$ 5 \) for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?

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.

asymptotes of \( f \).

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.

\( ( e ^ { x } - \sin y ) d x + ( \cos y ) d y \)

MAS182 - Applied Mathematics 13. Final Examination - S1 2021 The water content \( W(t) \) (measured in grams) in the cheese is governed by the differential equation \[ \frac{d W}{d t}=-(W-100)^{2} \] with initial condition \( W(0)=200 \mathrm{~g} \) and time is measured in hours.