Exam 13: Additional Differentiation Topics

Find if = + y

Find where y = ln .

The total revenue from the sales of a certain product are given by R(x)= .Find the marginal revenue.

Determine the point elasticity of the demand equation: q = - 10p + 200.

Find y' if 3 - 7 = 8.

Find if

The demand function for a manufacturer's product is given by p = 500 - 5q - where p is the price per unit when q units are demanded.The point elasticity of demand when q = 5 is

At a volleyball game concession stand,the profit P from selling x number of T-shirts (in hundreds)is given by P = 8x - 4x ln x.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.

Determine the point elasticity η of the demand equation p = -3q + 120,where p > 0 and q > 0.

If the point elasticity of demand for a product is -2.3 and the price of the product increases 3%,what is the approximate percentage decrease in demand?

Differentiate: g(x)=

Find y' if y = ln .

Find the point elasticity of the demand equation p = 15 - 0.3q for the value q = 300,and determine whether demand is elastic,inelastic or has unit elasticity.

Use your graphing calculator to graph the equation y = + 3 + + + x - 1.Zoom in on the graph to approximate the roots of the equation.Use Newton's method to verify your results.

If y = ,then find y'.

An experiment was set up to find a relationship between weight and systolic blood pressure in children.It was found that p(x),the systolic blood pressure,was approximately p(x)= 17.5(1 + ln x),where x is the child's weight in pounds.Find p'(x).

Use Newton's method to approximate the root of + 5x - 1 = 0 that lies between 0 and 1.Continue the approximation procedure until the difference of two successive approximations is less than 0.0001.

Find if

Use logarithmic differentiation to find from y = .

If f(x)= ,find the rate of change of f'.