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6:04Economics
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?
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.
Understanding Motion from Graphs
The accompanying figure shows the velocity v = f(t) of a particle moving on a horizontal coordinate line.
c. When does the particle move at its greatest speed?
Understanding Motion from Graphs
The accompanying figure shows the velocity v = f(t) of a particle moving on a horizontal coordinate line.
d. When does the particle stand still for more than an instant?
In Exercises 19–22, find the values of the derivatives.
dr/dθ |θ₌₀ if r = 2/√(4 – θ)
