Exam 12: Differentiation

Suppose that the profit p made by selling a certain product at a price x is given by p = f(x)and the rate of change of that profit with respect to change in price is = 8 at x = 3.Estimate the change in the profit p if the price changes from 3.5 to 4.5.

Differentiate: f(x)=

A manufacturer will sell N(x)cars after spending $x thousand on advertising,where N(x)= 1000 - .Find the equation of the tangent line to this curve when x = 20.

If the velocity function is given by V(x)= 7 + 5x + 1,find an equation of the tangent line to the graph of V(x)at (0,1).

If the velocity function is given by V(x)= 12x - ,find an equation of the tangent line to the graph of V(x)at

If an object moves horizontally according to x = 5t - 2 and vertically according to y = 2 + x,find its vertical speed, .

Find (u)where f(u)=

The demand D for a product at price x is given by D = +40.Find and discuss what happens at x = 1.

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

If f(x)= ,then find f' (x)and determine whether or not f'(x)exists for all values of x.Use your graphing calculator to graph f(x).Use this graph to describe the behavior of the tangent line to f(x)at

If y = ,then y' =

If a manufacturer's average cost equation is = 200 + ,find the total cost function c,and the marginal cost function .What is the marginal cost when 17 units are produced?

The demand D for a product at price x is given by D = + 20.Find and graph the result on your graphing calculator.What is the behavior of the graph when x = 0?

Find all values of x for which the curve y = 6 + 4x - 5 has slope 2.

Find if y = + .

The demand equation for a manufacturer's product is p = 400 - ,where p is the price per unit for q units.Find the marginal revenue function.

If f(x)is defined by f(x)= ,then use your graphing calculator to graph the functions g(x)= and h(x)= x to determine: (a)if f(x)is continuous for all values of x. (b)if f(x)is differentiable for all values of x.

Differentiate: g(x)=

If the revenue function is given by R(x)= 5x - 7,find the derivative of the revenue function (this is called the marginal revenue).

Differentiate: g(x)=