Exam 2: Extension A: Limits and Derivatives

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

Use the definition of the derivative to find

Find the derivative of the function.

Find an equation of the tangent line to the parabola at the point

Find the slope of the tangent line to the curve at the point

If a cylindrical tank holds 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 an equation of the tangent line to the curve at the point (2,6).

The cost (in dollars)of producing x units of a certain commodity is Find the instantaneous rate of change with respect to x when x=103. (This is called the marginal cost.)

The cost (in dollars)of producing x units of a certain commodity is Find the average rate of change with respect to x when the production level is changed from