Chapter 4 and 5 Jeopardy

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Insight Questions

Finding the Derivative

Applications of Derivatives

Chapter 5

Final Jeopardy

QuestionAnswer

A-100

If f’(x) = g’(x), then what can you say about f(x) and g(x)?

QuestionAnswer

A-200

Sketch a graph who has the following properties:

Explain your graph

(3) 0

' 0 for 3

' 0 for 3

f

f x

f x

QuestionAnswer

A-300

1If ( )

find '( )

nf x

xf x

QuestionAnswer

A-400

Sketch the function:

Then sketch and explain f’(x).

3 2( ) 3 3f x x x x

QuestionAnswer

A-500

State and explain the formal definition of a derivative. Use a graph in your explanation.

QuestionAnswer

B-100

Find the derivative:

2

4( )

(3 )f x

x

QuestionAnswer

B-200

Find the derivative of the function:

1( )f x x

x

QuestionAnswer

B-300

Find the derivative of the function by using the definition of the derivative:

2( )f x

x

QuestionAnswer

B-400

Find the derivative of the function:

52 1

( )f x xx

QuestionAnswer

B-500Use implicit differentiation to find the derivative:

2 2( )( )y x y x y

QuestionAnswer

C-100

The edges of a cube are expanding at a rate of 3 cm per second. Find the rate of change of the volume of a cube with sides of 4 cm

QuestionAnswer

C-200

Find the rate of change of the distance between the origin and a moving point on the graph of

if 2 cm/secdx

y xdt

QuestionAnswer

C-300

The radius of a right circular cylinder is given by

Where t is time in seconds and dimensions are in inches. Find the rate of change of the volume with respect to time.

12 and its height is ,

2t t

QuestionAnswer

C-400

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius of the outer ripple is increasing at a constant rate of 2 foot per second. When the radius is 4 feet, at what rate is the total area of the disturbed water changing?

QuestionAnswer

C-500

A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. Water is flowing into the tank at a rate of 10 cubic feet per minute. Find the rate of change of the depth of the water when the water is 8 feet deep.

QuestionAnswer

D-100

If Rolle’s Theorem can be applied, find all values of c in the open interval (a, b) such that f’(c)=0

2 1( ) , ( 1,1)

xf x

x

QuestionAnswer

D-200

23

Find the extrema of

( ) 2 3

on the interval 1,3

f x x x

QuestionAnswer

D-300

Find the point(s) guaranteed by the Mean Value Theorem for the closed interval [a, b]

( ) 2 0, 4f x x x

QuestionAnswer

D-400

(a)Find the critical numbers of f(b)find the open intervals on which the function

is increasing or decreasing(c)Apply the First Derivative Test to identify all

relative extrema

3 2( ) 2 3 12f x x x x

QuestionAnswer

D-500

(a)Find the critical numbers of f(b)find the open intervals on which the function

is increasing or decreasing(c)Apply the First Derivative Test to identify all

relative extrema

2 3( ) 3( 2) 2 4f x x x

QuestionAnswer

FINAL JEOPARDY

Use symmetry, extrema, and zeros to sketch the graph of f

6 4 2

2

5 6( )

2

x x xf x

x