Calculus Quiz 3.1-3.4 Derivatives Name

Calculus Quiz 3.1-3.4 Derivatives Name

1.  Use the definition of derivative to prove that the derivative of is .

Definition of Derivative :

2.  Let

a.  Approximate using a symmetric difference quotient (make a table of values). Let

b.  Evaluate algebraically (using the power rule).

c.  How close an approximation did you find in part ( a)?

Calculus Quiz 3.1-3.4 Derivatives page 2

3.  Find the derivative of each function. Use the algebraic method (notice the various ways of representing functions and their derivatives). Show any work.

a.  ;

b.  ;

c.  ;

d.  ;

e.  ;

f.  ;

4.  The graph shows the function .

a. Evaluate algebraically.

b.  Find the y-coordinate of . On the graph, draw a line with slope of that passes through the point . How is the line related to the graph?

c.  Write an equation for the line you drew in part (b).

Calculus Quiz 3.1-3.4 Derivatives page 3

5.  In each of the following, the graph of a function f(x) is given. Select the correct graph of f'(x). Draw a line from the graph to its derivative.

a.

1. Graph of y = f(x):
/ 2. Graph of y = f(x):

Graph of f'(x) (Select One)
/ /
/ /

Calculus Quiz 3.1-3.4 Derivatives page 4

b.

3. Graph of y = f(x):
/ 4. Graph of y = f(x):

Graph of f'(x) (Select One)
/ /
/ /

BONUS QUESTIONS: 1 point each:

1)  A man and his son are in a car crash. The father is killed and the child is taken to hospital gravely injured. When he gets there, the surgeon says, 'I can't operate on this boy - for he is my son!!!' How can this possibly be?

2)  Acting on an anonymous phone call, the police raid a house to arrest a suspected murderer. They don't know what he looks like but they know his name is John and that he is inside the house. The police bust in on a carpenter, a lorry driver, a mechanic and a fireman all playing poker. Without hesitation or communication of any kind, they immediately arrest the fireman. How do they know they've got their man?

3)  Five pieces of coal, a carrot and a scarf are lying on a hill near a remote house. Nobody put them on the lawn but there is a perfectly logical reason why they should be there. What is it?