2. (10 pts) The productivity of a South American country is given by the function \[ f(x, y)=12 x^{0.35} y^{0 . s s} \] when \( x \) units of labor and \( y \) units of capital are used. What is the marginal productivity of labor and the marginal productivity of capital when the amounts expended on labor and capital are 120 units and 30 units, respectively?

10. Evaluate \( \lim _{x \rightarrow 0} \frac{\tan x-\sin x}{x^{3}} \)

Determina el punto móximo de la función \( f(x)=2 x^{3}-9 x^{2}+15 \) NOTA: Escribir la respuesta en coordenadas, ejemplo \( (x, y) \)

Es el punto de inflexión de la función \( \mathrm{f}(\mathrm{x})=2 \mathrm{x}^{3}-12 \mathrm{x}^{2}+6 \mathrm{x}-3 \) NOTA: Escribe el resultado en coordenadas, ejemplo \( (x, y) \)

Suppose that the function \( f \) is defined for all real numbers as follows. \[ f(x)=\left\{\begin{array}{ccc}-x^{2}+10 & \text { if } & -4 \leq x<4 \\ 6-3 x & \text { if } & x \geq 4\end{array}\right. \] Graph the function \( f \). Then determine whether or not the function is cont

The formula \( D=50 e^{-0.4 h} \) can be used to find the number of milligrams \( D \) of a certain drug that is in a patient's bloodstream \( h \) hours after the drug was administered. When the number of milligrams reaches 3 , the drug is to be administered again. What is the time between injections? The time between injections is (Round to two decimal places as needed.).