Una empresa prestadora de salud desea fabricar una cantidad Optima de cierto medicamento. La función que modela el costo t (en miles de dólares) de fabricar \( x \) unidades del medicamento es \( C(x)=0.02 x^{\wedge} 3-0.6 x^{\wedge} 2+6 x+10 \). ¿Cuântas unidades del medicamento deben fabricar para minimizar el costo total? a. 15 b. 20 c. 10 d. 5

2. \( y=\frac{3^{\sqrt{x}}}{\lg (3-x)} \)

2) La ecuación del movimiento de una particula está dada por: \( s(t)=t^{3}-3 t \) Encontrar: a) La velocidad como función de \( t \) b) La aceleración después de 4 segundos. c) la aceleración cuando la velocidad es cero.

A national fast food company has just analyzed the effect of the latest sales promotion. It has determined that the sales decay for its milkshakes is given by \( S=285,000 e^{-0.7 x} \), where \( S \) is the weekly sales and \( x \) is the number of weeks that have passes since the end of the sales promotion. a) Determine the sales 2 weeks after the end of the promotion: Round answer to 2 decimal places. Sales \( =\$ \) b) If no new campaign is started, how many weeks after the end of the promotion will sales drop below 30,000 ? Round answer to 1 decimal place. Num. weeks =

7. c) \( \frac{1}{1+x}-\frac{2}{x^{2}-1} \)

Find the average rate of change of \( h(x)=-2 x^{2}-5 x \) from \( x=-4 \) to \( x=1 \). Simplify your answer as much as possible.