Exam 13: Additional Differentiation Topics

If f(x)= (2x - ,find f'''(x).

If the demand equation for a product is q = ,where q is the number of units demanded at price p per unit,find the elasticity of demand when p = 48.

If the total profit (in dollars)from the sale of x dishwashers is P(x)= 40x - 0.02 - 1000 + 2 ln(x),use Newton's method to approximate the break-even points for profit.(Note: There are 2 break-even points; one is between 10 and 50,and the other is between 1900 and 2000.)

If y = + ,then find y'.

Use your graphing calculator to graph the equation y = - + x.Zoom in on the graph to approximate the roots of the equation.Use Newton's method to verify your results.

If the position of a particle moving along the x-axis at a given time is given by x(t)= 5t + 11,find all the higher-order derivatives of this function.

If f(x)= 8 - 6 + 7x - 2,find f'''(x).

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

Determine the point elasticity η of the demand equation pq + p + 50q = 10,000 when p = 200.

If 2 - xy + = 4,then =

Use logarithmic differentiation to find from y = ( + x + .

If y = ,find .

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

At a football game concession stand,the profit P from selling x number of T-shirts (in hundreds)is given by Find .Use your graphing calculator to graph both P and on the same set of axes.Verify that when the graph of P reaches its peak,the graph of crosses the x-axis.

A shoe company is planning a new brand of walking shoe for the market.Research shows that x,the number of shoes sold (in thousands)at a price of $p,can be approximated by x = -2ln where Find .

For an isosceles right triangle,the length of the hypotenuse h is related to the length of a side x by Find ,the rate of change of the hypotenuse with respect to to a side.

If y = e ,then find y'.

An approximation of one root of - 2 + 5 is = 1.Apply Newton's method twice to find an approximation to the root of the polynomial.

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

Determine the point elasticity η of the demand equation + 3p + q = 72,when p = 5.