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Calculus BC - Chapter 2 Review (Differentiation)



1.
Find the derivative of the following function using the limiting process.


Answer:


2.
Find an equation of the line that is tangent to the graph of f and parallel to the given line.



A.
B.
C.
D.
E.
None of the above


3.
Find the derivative of the function.


A.
B.
C.
D.
E.
None of the above


4.
Find the slope of the graph of the function at the given value.

when
A.
B.
C.
D.
E.


5.
Find the slope of the graph of the function at the given value.

when
A.
B.
C.
D.
E.


6.
Determine the point(s), (if any), at which the graph of the function has a horizontal tangent.



A.
B.
and
C.
and
D.
E.
There are no points at which the graph has a horizontal tangent.


7.
A ball is thrown straight down from the top of a 290-ft building with an initial velocity of –20 ft per second.

What is its velocity after 1 seconds?

What is its velocity after falling 110 ft?

The position function is .
A.
Its velocity after 1 seconds is –12 ft per second. After falling 110 ft its velocity is about 86.26 ft per second.
B.
Its velocity after 1 seconds is –52 ft per second. After falling 110 ft its velocity is about 86.26 ft per second.
C.
Its velocity after 1 seconds is –52 ft per second. After falling 110 ft its velocity is about –86.26 ft per second.
D.
Its velocity after 1 seconds is –12 ft per second. After falling 110 ft its velocity is about –86.26 ft per second.
E.
None of the above


8.
Use the quotient rule to differentiate.


A.
B.
C.
D.
E.


9.
Find the derivative of the algebraic function.



A.
B.
C.
D.
E.


10.
Find the derivative of the function.


A.
B.
C.
D.
E.


11.
The length of a rectangle is and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time.

A.
square inches/second
B.
square inches/second
C.
inches/second
D.
inches/second
E.
square inches/second


12.
Find the second derivative of the function.


A.
B.
C.
D.
E.


13.
Find the derivative of the function.


A.
B.
C.
D.
E.


14.
Find an equation to the tangent line to the graph of f at the given point.

,

The coefficients below are given to two decimal places.
A.
B.
C.
D.
E.


15.
Find dy/dx by implicit differentiation.


A.
B.
C.
D.
E.


16.
Find an equation of the tangent line to the graph of the function given below at the given point.

    .

(The coefficients below are given to two decimal places.)
A.
B.
C.
D.
E.


17.
Shadow Length A man 6 feet tall walks at a rate of 2 ft per second away from a light that is 15 ft above the ground (see figure). When he is 10 ft from the base of the light find the following.

(a) The rate the tip of the shadow is moving.
(b) The rate the length of his shadow is changing.

 
(a)
(b)
 
A.
  ft per minute
 
ft per minute
 
B.
 
ft per minute
ft per minute
 
C.
 
  ft per minute
ft per minute
D.
 
ft per minute
ft per minute
 
E.
None of the above


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