Exam 12: Differentiation

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

Money is invested in an annuity that earns r percent per year,compounded monthly.The future value S of $500 invested in such an annuity for 4 years is S = 500 .Find S'.

Suppose the position function of an object moving along a number line is given by s = f(t)= + 2 + 5,where t is in seconds and s is in meters. (a)Find the average velocity over the interval . (b)Find the velocity when t = 2.

A cardboard container in the shape of a cube is being filled with coffee beans.Find the rate of change of the volume with respect to the length of a side of the cube.Evaluate this rate of change when a side is 5 inches long.

A radio station charges its advertisers $75 per commercial.Each advertiser must purchase lat least 100 commercials.The station offers to discount the per-commercial charge by $0.30 for each additional commercial purchased above 100.The revenue for the radio station is given by: where x is the number of additional commercials above 100.Find the marginal revenue function using the product rule.

Find if y = .

If the velocity function is given by V(x)= 3x - ,find an equation of the tangent line to the graph of V(x)at

Find if y = - + 4x - 6.

If y = ,then =

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

Suppose that c = 0.008 - + 80q + 20,400 is a cost function,where c is the total cost in dollars of producing q units of a product.Find the marginal cost when q = 10.

Find if y = - .

Find if y = .

A person x inches tall has a pulse rate of y beats per minute,as given approximately by y = Find .

Find y' if y = .

Differentiate: g(x)=

The average cost of producing q units of a product is given by = + .Find the marginal cost function.

If the profit for a stereo company (in thousands of dollars)is given by the equation find the slope of the tangent to this curve at (2,33).

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

During the morning commute,the average speed of a vehicle on the highway is given by where t is the number of hours after 6:00 a.m.Rewrite this function so that all terms are in the form .