Exam 13: Additional Differentiation Topics

Determine the point elasticity η of the demand equation 3 q = 5000 + 2000 ,when p = 50.

Suppose that the supply of q units of a product at price $p is given by q = 10 + 25 ln p.Find .

Suppose the number of fleas N (in thousands)in a given area is related to the number of pounds of insecticide x sprayed on the nesting areas according to Nx - 10x + N = 300.Find ,the rate of change of the number of fleas with respect to the number of pounds of insecticide.

If the total profit (in dollars)from the sale of x lawn mowers is P(x)= 30x - 0.03 - 750 + ln(x),use Newton's method to approximate the break-even points for profit.(Note: There are 2 break-even points; one is between 0 and 40,and the other is between 900 and 1000.)

If f(x)= ,then f'(x)=

Suppose p = 500 - 0.01q - 0.02 is the demand equation for a product.Find the rate of change of quantity with respect to price.

Suppose the number of fleas N (in thousands)in a given area is related to the number of pounds of insecticide x sprayed on the nesting areas according to Nx - 9x + N = 250.Find ,the rate of change of the number of fleas with respect to the number of pounds of insecticide.

The height h(t)of a rock dropped off of a 200 foot building is given by h(t)= 200 - 16 ,where t is the time measured in seconds.Find ,the acceleration of the rock,when t = 3.

An approximation of one root of - 2 + 5 is = 1.5.Apply Newton's method twice to find an approximation to the root of the polynomial.

Differentiate: f(x)=

The demand function for a manufacturer's product is given by p = 20 - 0.02q,where p is the price per unit when q units are demanded.The point elasticity of demand when q = 100 is

At a soccer game concession stand,the profit P from selling x number of T-shirts (in hundreds)is given by Find .

If y = ,logarithmic differentiation gives y' =

Differentiate: g(x)= 4x

Use Newton's method to approximate the root of - 6x + 1 = 0 that lies between 0 and 1.Continue the approximation procedure until the difference of two successive approximations is less than 0.0001.

If f(x)= ,then f'(x)=

If y = ,use logarithmic differentiation to find y'.

In psychology,the Weber-Fechner law for stimulus response is R = k ln where R is the response,S is the stimulus,and is the lowest level of stimulus that can be detected.Find .

The location of an Earth-orbiting satellite in a grid centered at the center of the Earth is given by Find .

If y = (4x - ,use logarithmic differentiation to find y'.