Exam 12: Differentiation

If the revenue for a certain company is given by R(x)= 500,find .

Determine the relative and percentage rates of change of y = f(x)= + 5x + 2 when x = 1.

The position of an object thrown upward at a speed of 32 feet/sec from a height of 200 feet is given by: Find the rate of change of y with respect to t and evaluate it when t = 1 and t = 2.Interpret your results.

A soda stand usually sells 400 sodas per day at $0.70 each.A business student's research tells her that for every $0.10 decrease in price,the stand will sell 55 more sodas per day.The revenue function for the soda stand is given by: R(x)= (0.70 - 0.1x)(400 + 55x)where x is the number of $0.10 reductions in price.Find ,the marginal revenue.

A value of x for which the slope of the curve y = - + 2x + 1 is zero is

Find the derivative of y = .

A cylindrical tank has a height of 7 inches.It is being filled with syrup.Find the rate of change of its volume with respect to the radius of the cylinder.Evaluate this rate of change when the radius is 2 inches.

If the demand equation is D(x)= 2 + ,then find an equation of the tangent to this curve when x = 3.Use your graphing calculator to verify that this line is tangent to D(x)when x = 3.

Find if y = (9x + 3).

If f(x)= ,then the percentage rate of change of f(x)when x = 3 is

Suppose the cost of a product can be approximated by c = - 2x + 22.Find the derivative of this function to determine whether or not this function is continuous for all values of x.

One hour after x milligrams of a particular drug are given to a person,the change in body temperature T(x),in the degrees Fahrenheit,is given approximately by T(x)= .The rate at which T changes with respect to size of dosage x,T'(x),is called the sensitivity of the body to the dosage.Use the product rule to find the slope of T(x)when the dosage is 3 milligrams.

Use the Chain Rule to find where y = - 8u + 5; u = - 11x + 5.

Find where y = .

Find y' if y = .

Suppose that the demand for candy at a price of $p per pound is given by the equation Find (p)when p = 10.

A particle travels along a straight line path according to the equation of motion s = + 3t + 4,where t is in seconds and s is in meters.The velocity (in meters per second)of the particle at t = 2 is

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

Find the slope of the curve y = at the point where x = 3.

If a manufacturer's average cost equation is = 500 + 15q + ,find the total cost function c,and the marginal cost function .What is the marginal cost when 10 units are produced?