If y = x² and dx/dt = 3, then what is dy/dt when x = –1?

Economics

Marginal cost Suppose that the dollar cost of producing x washing machines is c(x) = 2000 + 100x − 0.1x².

c. Show that the marginal cost when 100 washing machines are produced is approximately the cost of producing one more washing machine after the first 100 have been made, by calculating the latter cost directly.

Economics

Marginal revenue

Suppose that the revenue from selling x washing machines is

r(x) = 20000(1 − 1/x) dollars.

b. Use the function r'(x) to estimate the increase in revenue that will result from increasing production from 100 machines a week to 101 machines a week.

Economics

Marginal revenue

Suppose that the revenue from selling x washing machines is

r(x) = 20000(1 − 1/x) dollars.

c. Find the limit of r'(x) as x → ∞. How would you interpret this number?

Assume that y = 5x and dx/dt = 2. Find dy/dt

If x = y³ – y and dy/dt = 5, then what is dx/dt when y = 2?

If x²y³ = 4/27 and dy/dt = ¹/₂, then what is dx/dt when x = 2?

If L = √(x² + y²), dx/dt = –1, and dy/dt = 3, find dL/dt when x = 5 and y = 12.

If r + s² + v³ = 12, dr/dt = 4, and ds/dt = –3, find dv/dt when r = 3 and s = 1.