Exam 12: Differentiation

If the formula for the wind-chill,W,at 15° is given by W = 55.174 - 2.15s - 23.18 ,find the derivative of this formula.

If the profit for a cat food company (in hundred of dollars)is given by the equation P(x)= 178x - ,use the derivative function on your graphing calculator to find the slope of the tangent to this curve at

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

Find the slope of the curve y = at the point (3,2).

Find if y = (0.00 .

The revenue R from the sale of x units of a product is R = + 18x.The number of units sold after t weeks of advertising is x = 20 + .Find when t = 6.

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

Find if y = + ln 2.

Find the slope of the curve y = ( + 2x - at the point (0,16).

If the cost function for a manufacturer's product is given by C = ,find the marginal cost function.

The cost of producing x number of objects is given by C(x)= 5x + .Determine the relative and percentage rates of change of cost with respect to x when 10 objects are made.

Find if y = - + 7x - 8.

Find the equation of the tangent line to the graph of the curve y = 2 + 3x + 11 at the point (0,11).

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

If the velocity function is given by V(x)= + 12.3,find an equation of the tangent line to the graph of V(x)at (2.47,67.2801).Use your graphing calculator to verity that the graph of V(x)and the tangent line are at the point (2.47,67.2801).

The derivative of the revenue function (the marginal revenue function)for a product is given by .Use this information to determine if the revenue equation is continuous for all values of x.

Let p = 10,000 - 12 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 = 9? Assume that p is in dollars.

If the revenue function is given by R(x)= 11x + 9,find the derivative of the revenue function (this is called the marginal revenue).

If y = - 8 + 2u - 1 and u = ,find When x = -9.

For a particular host-parasite situation,the number y of hosts that are parasitized when the host density is x is given by y = .At what rate is the number of hosts parasitized changing with respect to host density when x = 2?