The function \( \mathrm{D}(\mathrm{h})=2 e^{-0.64 \mathrm{~h}} \) 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 has been administered. How many milligrams will be present after 1 hour? After 12 hours? After 1 hour, there will be \( \square \) milligrams. (Round to two decimal places as needed.)

Find the point(s) at which the function \( f(x)=10-|x| \) equals its average value on the interval \( [-10,10] \) The function equals its average value at \( x=\square \) (Type an integer or a fraction. Use a comma to separate answers as needed.)

49. Marginal Productivity A manufacturer estimates that produc- tion (in hundreds of units) is a function of the amounts \( x \) and \( y \) of labor and capital used, as follows. \[ f(x, y)=\left(\frac{1}{4} x^{-1 / 4}+\frac{3}{4} y^{-1 / 4}\right)^{-4} \] a. Find the number of units produced when 16 units of labor and 81 units of capital are utilized. b. Find and interpret \( f_{x}(16,81) \) and \( f_{y}(16,81) \). c. What would be the approximate effect on production of increasing labor by 1 unit from 16 units of labor with 81 units of capital? 50. Marginal Productivity The production function \( z \) for the United States was once estimated as where \( x \) stands for the amount of labor and \( y \) the amount of capital. Find the marginal productivity of labor and of capital.

Resuelve la ecuación diferencial \( \frac{dy}{dx} = 3y^{2} \) dado que \( y(0) = 1 \).

Given the following velocity function of an object moving aiong a line, find the position function with the given initial position. \[ v(t)=2 \sqrt[3]{t}, s(0)=3 \] The position function is \( s(t)=\square \)

\( \int \frac { 3 x ^ { 5 } } { \sqrt { 7 - 12 x ^ { 6 } } } d x = \square \)