Exam 12: Differentiation

Find y' if y = (2x - .

The demand D for a product at price x is given by D = -5.2 + 22.Find and graph the result on your graphing calculator.What is the behavior of the graph when x = 0?

Find y' if y = .

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 7 milligrams.

By direct use of the definition of derivative,find (f(x))if f(x)= 3 + 5x - 4.

Find if y = .

Find the derivative of y = ( + + 1)(5 + 7 + 1).

The revenue R from the sale of x units of a product is R = + 50x.The number of units sold after t weeks of advertising is x = 48 + .Find when t = 4.

Find if y = e.

If the output function is given by Q(x)= 150 + ,find the slope of the curve at the point where x = 25.

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

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

Differentiate: f(x)=

Find if y =

The position of an object thrown upward from a height of 100 feet/sec from a height of 40 feet is given by: Find the rate of change of y with respect to t and evaluate it when t = 1 and t = 4.Interpret your results.

A cylindrical tank has a radius of 3 feet.It is being filled with water.Find the rate of change of its volume with respect to the height of the cylinder.Evaluate this rate of change when the height is 7 ft.

Find if y = .

When a ball is thrown upward at a speed of 60 feet/s from a height of 500 feet,its height H in feet after is given by H = 500 + 60t - .Find .

Find the derivative of x = f(x)= ( + - 18t +11)( + - 17t + 5).

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 4 milligrams.