BUCKET-BALL2.1 – 2.3 Review

1. You need a piece of paper and a pencil.2. Write your TEAM NUMBER, your NAME, and your

LETTER(A-D) on the top of your paper.3. For each question I will call one letter to come and

show their solution (INCLUDING ALL NECESSARY WORK).

4. 1 point is awarded for a correct answer. 5. If a team gets an answer correct they can shoot a

basket for 1 bonus point.

NOT PARTICIPATING WILL COST YOUR TEAM POINTS.

RULES

Find the derivative, and simplify:

#1

2 3

6x xf x

#1 ANSWER

1 1( )3 2

f x x

Find the derivative and simplify.

#2

#2 ANSWER

4 2( ) 5 3 2f x x x

An automobile’s velocity (ft/s), starting from rest, is represented by

Find the acceleration of the automobile at .

#3

#3 ANSWER

260 ft(10) 1.224

sec49a

#4Find the second derivative and simplify:

23( ) 2 3f x x

#4 ANSWER

4120 72f x x x

#5If the nth derivative of y is denoted as and , then what is

#5 ANSWER

20 2siny x

#6Evaluate the limit:

0

sin sin2 2lim

h

h

h

#6 ANSWER

cos 02

This is asking to find the derivative of sinx when x=pi/2

#7If, which of the

following must be true?

I. f is continuous at x = 2.II. f is differentiable at x = 2.III. (2) 5f

2lim ( ) 5x

f x

#7 ANSWER

None need to be true.

#9Find the values of a and c that make the function differentiable at

2 sin , ( )

2 , ax x x

f xx c x

#9 ANSWER

#10

X

1 3 1 4

2 5 3 1

3 2 1 14 4 2

Let

Find

#10 ANSWER

#11Find the equation of the tangent line to the function

at the point when

#11 ANSWER

𝑦−6=6√3(𝑥− 𝜋3 )

#12

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

#12 ANSWER

4 325 16dA t tdt