Exam 12: Differentiation

A cone has a height of 10 inches.It is being filled with ice cream.Find the rate of change of its volume with respect to the radius of the base of the cone.Evaluate this rate of change when the radius is 12 inches.

Suppose the position function of an object moving along a line is given by s = f(t)= - 3t + 7 where t is in seconds and s is in feet. (a)Find the average velocity over the interval . (b)Find the velocity when t = 5.

Let f(x)= - 6x + 7. (a)Find f '(x). (b)Evaluate f '(2). (c)Find an equation of the tangent line to the graph of y = f(x)at the point (2,3).

If the height of an eaglet sitting in a nest is given by y = 324,find .

An equation of the tangent line to the curve y = 4 - 6x - 5 at the point (-1,5)is

If y = f(x)= - 2x + 2,find the (a)relative and (b)percentage rate of change of y when x = 4.

Find the equation of the tangent line to the graph of the curve at the point (0,0.0095).

Suppose that the cost C of processing the contaminated water at an industrial site so that only p percent of the contaminants escape is given by C(p)= .Find without using the quotient rule.

If y = - 13u + 3 and u = + + 4x -14,then by direct use of the chain rule find and evaluate when

Find y' if y = .

If p = - 9m + 3,then the rate of change of p with respect to m when m = 1 is

If g(x)= (2x - ,then g'(1)=

Suppose the position function of an object moving along a number line is given by s = f(t)= 2 + 11,where t is in seconds and s is in meters. (a)Find the average velocity over the interval . (b)Find the velocity when t = 3.

For the consumption function C = 10 + I - , (a)find the marginal propensity to consume when I = 16; (b)find the marginal propensity to save with I = 16.

The demand D for a product at price x is given by D = - 1.Find and discuss what happens at x = 0.

If the profit for a toy company (in millions of dollars)is given by the equation P(x)= 4x - ,find the slope of the tangent to this curve at (1,3).

If an object moves horizontally according to x = 3t - 5 and vertically according to y = 3 ,find its vertical speed, .

If the cost C of removing p percent of the impurities from the waste water in a manufacturing process is given by C(p)= ,find C'(p).

The demand for a product is given by p = .Does the derivative of this function exist for all values of q?

Differentiate: f(x)= 2x( + 6 )- 4(3 + x)(8x - 7)