Exam 12: Differentiation

The demand D for a product at price x is given by D = 8 .Find and discuss what happens at

Suppose the position function of an object moving along a number line is given by s = f(t)= + 5t,where t is in seconds and s is in meters. (a)Find the average velocity over the interval . (b)Find the velocity when t = 7.5.

A catering company will plan a group dinner for groups of 20 or larger.If the group is exactly 20,the cost is $15 per person.The company offers to discount each person's ticket by $0.50 for each addition to the group above 20.The revenue for the catering company is given by: R(x)= (20 + x)(15 -0.5x)where x is the number of additional people above 20.Find the marginal revenue function using the product rule.

Suppose that the equation r= 430q - gives the total revenue r (in dollars)that a manufacturer receives when q units of a product are sold.Determine the marginal revenue when q = 100 and interpret your result.

Find if y = - + .

Find y' if y = 5( - 3x + .

Suppose the number of calories of heat required to raise 1 gram of water (or ice)from -40°C to x°C is given by Is this function differentiable for all values of x?

A particle travels along a straight line path according to the equation of motion s = + + 1,where t is in seconds and s is in meters.Find the velocity of the particle at t = 2.

By direct use of the definition of derivative,find (f(x))if f(x)= 4 - 5 .

Find all values of x for which the curve y = + has slope 1.

If the revenue function is given by R(x)= 10x,find the derivative of the revenue function (this is called the marginal revenue).

By direct use of the definition of a derivative,find if f(x)= .

Find if y = + .

The sales s of a product vary with the number of weeks of an advertising campaign according to Use the power rule to find .

Find if v = ( + 3t).

Find where z = + + 1; u = - 8s.

A stereo company sells 300 car stereos per month at a price of $280 per car stereo.Market research indicates that they can sell one additional stereo for each $1 they reduce the price.In this case the total revenue is given by: R(x)= (300 + x)(280 - x)where x is the number of additional stereos above 300.Find the marginal revenue function using the product rule.

If a manufacturer's average cost equation is = - 422q + ,find the total cost function c,and the marginal cost function .What is the marginal cost when 20 units are produced?

The position of an object thrown upward at a speed of 8 feet/sec from a height of 10 feet is given by: Find the rate of change of y with respect to t and evaluate it when t = 0.25.Use your graphing calculator to graph y(t).Use the graph to interpret the behavior of the object when t = 0.25.

If a manufacturer's average cost is given by = 0.001 - 0.12 + 7 + find (a)the marginal cost function; (b)evaluate it when 50 units are produced.