Exam 2: Derivatives

Gravel is being dumped from a conveyor belt at a rate of 32 ft/min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.How fast is the height of the pile increasing when the pile is 10 ft high? Round the result to the nearest hundredth.

Find an equation of the tangent line to the given curve at the indicated point.

The curve with the equation is called an asteroid.Find an equation of the tangent to the curve at the point ( ,1).

If a cylindrical tank holds 10000 gallons of water,which can be drained from the bottom of the tank in an hour,then Torricelli's Law gives the volume of water remaining in the tank after t minutes as Find the rate at which the water is flowing out of the tank (the instantaneous rate of change of V with respect to t)as a function of t.

Find the derivative of the function.

Find the derivative of the function. = 3 sin x + 9x - 9

Find equations of the tangent lines to the curve that are parallel to the line . a. b. c. d. e.

Determine the values of x for which the given linear approximation is accurate to within 0.07 at a = 0.

Find the derivative of the function.

Use the linear approximation of the function at to approximate the number .

A plane flying horizontally at an altitude of 1 mi and a speed of 520 mi/h passes directly over a radar station.Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

A baseball diamond is a square with side 90 ft.A batter hits the ball and runs toward first base with a speed of 32 ft/s.At what rate is his distance from second base decreasing when he is halfway to first base? Round the result to the nearest hundredth.

Differentiate.

Find the slope of the tangent line to the curve at the point (-4 , 22)

The top of a ladder slides down a vertical wall at a rate of 0.1 m/s .At the moment when the bottom of the ladder is 3 m from the wall,it slides away from the wall at a rate of 0.2 m/s .How long is the ladder?

If an equation of the tangent line to the curve at the point where

The cost (in dollars)of producing x units of a certain commodity is Find the instantaneous rate of change with respect to x when (This is called the marginal cost.)

Find an equation of the tangent line to the curve at the point (2 , 6)

If two resistors with resistances and are connected in parallel,as in the figure,then the total resistance measured in ohms ( $\Omega$ ),is given by . If and are increasing at rates of and respectively,how fast is changing when and ? Round the result to the nearest thousandth.

Use the definition of the derivative to find