Exam 12: Differentiation

Let p = 405 - be the demand function for a manufacturer's product.Find the rate of change of price p per unit with respect to quantity q.How fast is the price changing with respect to q when q = 4? Assume that p is in dollars.

Money is invested in an annuity that earns r percent per year,compounded monthly.The future value S of $3000 invested in such an annuity for 30 years is S = 3000 .Find S'.

The proportion P of voters who recognize the name of a certain candidate after t months of advertising is given by P(t)= .Find the equation of the tangent line to this curve when x = 1.Use your graphing calculator to verify that this line is tangent to P(t)when x = 1.

The position of an object dropped from a height of 200 feet is given by: y(t)= 200 - .Find the rate of change of y with respect to t and evaluate it when t = 1 and t = 2.Interpret your results.

The supply function for a computer company is given by f(x)= 3 + 20.Rewrite this function so that all terms are in the form .

Find all values of x for which the curve y = 2 - has a horizontal tangent line.

Find the slope of the curve y = at the point (11,1).

If a function is continuous at x = a,then it is differentiable at x = a.

The concentration of acid in a buffer solution is given by A = 0.8.Graph this function on your graphing calculator and describe its slope.

A certain factory emits sulfur dioxide into the atmosphere.The concentration C(x),in parts per million,is given by C(x)= where x is the distance from the plant in miles.What is (x)?

The typing speed of a certain computer student varies with the number of hours of practice x according to Find S'.

By using the definition of a derivative,find f(x)= .

By the definition of a derivative,the derivative of f(x)= is

If the profit for a car company (in thousands of dollars)is given by the equation 400 - ,find the slope of the tangent to this curve at (1,394).

Find if y = - .

When a ball is dropped from the top of a building,its speed after t seconds is given by 32t.What is (32t)?

If the distance in feet of a ball thrown from a bridge is given by D(t)= 30t + where t is the number of seconds after the ball is thrown,then the velocity of the ball is found by D(t).What is the velocity of the ball when t = 3?

A hot dog vendor sells chili dogs for $2.75 each.If she sells q chili dogs,the total revenue r is given by Find the marginal revenue.

An equation of the tangent line to the curve y = at the point where x = 5 is

The average cost for producing q units of a product is given by Find the marginal cost when q = 10.