Rachel M.

Use the guidelines of this section to sketch the curve.
$$y=x^{3}-12 x^{2}+36 x$$

Production A manufacturing firm estimates that its total production of automobile batteries in thousands of units is $$
f(x, y)=3 x^{1 / 3} y^{2 / 3}
$$
where $x$ is the number of units of labor and $y$ is the number of units of capital utilized. Labor costs are $\$ 80$ per unit, and capital costs are $\$ 150$ per unit. How many units each of labor and capital will maximize production, if the firm can spend $\$ 40,000$ for these costs?

For Exercises $1-12,$ determine whether the ordered pair is a solution for the equation.
$$(2,3) ; x+2 y=8$$

For Exercises $1-12,$ determine whether the ordered pair is a solution for the equation.
$$(3,1) ; 2 x-y=5$$

For Exercises $1-12,$ determine whether the ordered pair is a solution for the equation.
$$(-5,2) ; y-4 x=3$$

For Exercises $1-12,$ determine whether the ordered pair is a solution for the equation.
$$(4,-6) ; y=3 x-1$$