Raffle GameChapter 3.1-3.5 Review

Rules

• Get out two sheets of scratch paper. Tear them up into 6 even pieces each, for a total of 12 smaller pieces of paper.

• Put your name on each sheet. Make sure your name doesn’t take up the whole sheet of paper.

• When a problem comes up on the overhead, do the problem on one of your sheets, making sure to have the number problem written somewhere on the sheet.

• When you finish, put your sheet on the corner of your desk. If you get it right, you get to put the sheet into the raffle. If not, better luck next time.

• At the end of class, I will pull out 5 raffles. If your name is called, you’re a winner!

Problem 1

Use a limit definition of a derivative to find the derivative of

1( )4

f xx

Problem 2

Find the derivative of: 3

1 3 6 25

y xx x

Problem 3

Find the slope of the tangent line of at

( ) sin cosf x x x

2x

Problem 4

Find the derivative of tan

sec 3xyx

Problem 5

Is the following differentiable at x = 4? If not, then tell what type of non-differentiability is occurring there.

4( )

4x

f xx

Problem 6

Is the following differentiable at x = 0? If not, tell what type of non-differentiability is occurring there.

53( ) 4f x x

Problem 7

Find the equation of the normal line of at x = 3.

13 2xyx

Problem 8

Find the equations for the velocity, acceleration, and jerk if the position function is defined as: 6( ) coss t x

x

Problem 9

Given that the velocity of a particle represented by the function , is the particle speeding up or slowing down at t = 3?

2( ) 3 2 5v t x x

Problem 10

Given f(4)=3, f’(4)=-1, g(4)=7, g’(4)=-2, find the derivative of at x = 4. ( )

( )f xg x

Problem 11

Given f(4)=3, f’(4)=-1, g(4)=7, g’(4)=-2, find the derivative of at x = 4. 2 ( ) 4 ( )f x g x

Problem 12

Find the slope of the tangent line ofat x = 4.

4

13y xx