Deck 2: Extension A: Limits and Derivatives

Question 1

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

A)
B)
C)
D)
E) None of these

Answer 1

Question 2

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.

Answer 2

Question 3

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

A)
B)
C)
D)
E)

Answer 3

Question 4

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

A) 40
B) -40.
C) -40
D) 4
E) 25

Question 5

Use the definition of the derivative to find

A) -25
B) 25
C) 18
D) 27
E) does not exist

Question 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.)

A) 21.12
B) 23.18
C) 19.06
D) 19.06.
E) 4.12

Question 7

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

Question 8

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

A)
B)
C)
D)
E) None of these

Question 9

Find the derivative of the function.