Exam 13: Additional Differentiation Topics

Determine the point elasticity η of the demand equation (p + 1) = 1000,when p = 24.

An approximation of one root of - 2x - 3 = 0 is = 1)Apply Newton's method twice to find the approximation )

Suppose a population is growing according to the equation P = .Find the rate of growth of the population, .

The total sales x ( in hundred thousands)for a video cassette t months after the video is released can be approximated by x = .Use logarithmic differentiation to find .

If y = (ln ,then =

Find y' if xy = + 1.

Find y' if y =

Find if

Suppose that P,the proportion of people affected by a certain disease,is described by ln = 0.9t,where t is the time in months.Find ,at the rate at which P grows with respect to time.

If y = ln ,then y' =

Find y' if y = .

Find y' if ln(xy)+ y = 2.

Find where y = ( + 3x + 1).

The total revenue from the sales of a certain product are given by Find the marginal revenue.

Find an equation of the tangent line to the curve + + xy = 16 at the point (0,2).

The average cost for producing q units of product is given by = )At a production level of 900 units,the marginal cost is

Find y' if y =

Find y' if y = (x + .

Find if 3 + 7xy + = 19

If C(x),the cost to produce x units of a product,is C(x)= 4 + 13x + 8 and the marginal cost function is C'(x),then find the rate of change of the marginal function with respect to x when x = 9.