1. Find an equation for the line tangent to y= -5-5x^2 at (5,-130)
3. Using the defenition, calculate the derivative of the function:
Calculate: g'(-2), g'(1), g(sqrt 6)
4. Find y by applying the Product rule, and then find y by multiplying the factors to produce a sum of simpler terms to differentiate:
y=(3x^2 + 4) (2x-7+6/x)
5. Suppose that the dollar cost of producing x appliances is c(x)=1100 + 60x-0.2x^2.
(a) Find the average cost per appliance of producing the first 130 appliances.
(b) Find the marginal cost when 130 appliances are produced
(c) Show that the marginal cost when 130 appliances are produced is approximately the cost of producing one more appliance after the first 130 have been made, by calculating the latter cost directly.
This solution is comprised of detailed explanation and step-by-step calculation of the given problems and provides students with a clear perspective of the underlying concepts.