Chapter 3.3-3.5

Question 1

what is a derivative of a constant?

Answer 1

zero

Question 2

what is the power rule with and without a constant in front of the equation…

Answer 2

without: f(x) = x^n, then f’(x) = n x^n-1
with: f(x) = c x^n, then f’(x) =c n x^n-1

Question 3

what is the product rule?

Answer 3

d/dx (uv)= (u’v+uv’)

Question 4

what are all the other notation for the first derivative? (5)

Answer 4

1. f’(x)
2. dy/dx
3. d/dx y
4. d/dx f(x)
5. y’

Question 5

what are all the other notation for the second derivative? (3)

Answer 5

1. f’‘(x)
2. d^2y/dx
3. y’’

Question 6

what do you do when it asks for the derivative of pi?

Answer 6

it is just zero

Question 7

what does “find the horizontal tangent(s)” mean?

Answer 7

means find x when the derivative equation equals zero

Question 8

what does it mean when it asks for the slope of a tangent parallel to the x axis?

Answer 8

slope is zero

Question 9

what equation do you use when it asks you to make an equation from slope and an ordered pair?

Answer 9

y-y1 = m (x-x1)

Question 10

when the derivative curve is at y=0 what does this mean?

Answer 10

this is a maximum or minimum of the original equation

Question 11

what is the derivative of sinx?

Answer 11

cosx

Question 12

what is the derivative of cosx?

Answer 12

-sinx

Question 13

what is the derivative of tanx?

Answer 13

sec^2x

Question 14

what is the derivative of cscx?

Answer 14

-cscx * cotx

Question 15

what is the derivative of secx?

Answer 15

secx* tanx

Question 16

what is the derivative of cotx?

Answer 16

-csc^2x

Question 17

position is (original equation, 1st derivative, 2nd derivative, or 3rd derivative?)

Answer 17

original equation

Question 18

velocity is (original equation, 1st derivative, 2nd derivative, or 3rd derivative?)

Answer 18

1st derivative

Question 19

acceleration is (original equation, 1st derivative, 2nd derivative, or 3rd derivative?)

Answer 19

2nd derivative

Question 20

jerk is (original equation, 1st derivative, 2nd derivative, or 3rd derivative?)

Answer 20

3rd derivative

Question 21

what is the equation for displacement?

Answer 21

change in s = f(change in time) -f(start time)

Question 22

what is the equation for average velocity?

Answer 22

average velocity= (f(change in time) -f(start time))/ change in time

Question 23

what is the equation of speed?

Answer 23

it is just the absolute value of the velocity equation

Question 24

when velocity hits zero what does this mean?

Answer 24

means change in direction

Question 25

how do you know if a particle is moving to the left?

Answer 25

negative velocity (negative slope)

Question 26

how do you know if a particle is moving to the right?

Answer 26

positive velocity (positive slope)

Question 27

how do you know if a particle is standing still?

Answer 27

when velocity is zero

Question 28

how do you know if a particle is speeding up?

Answer 28

velocity and acceleration have the same sign

Question 29

how do you know if a particle is slowing down?

Answer 29

velocity and acceleration have different signs

Question 30

cosx is the value of …

Answer 30

the x coordinate

Question 31

sinx is the value of …

Answer 31

the y coordinate

Question 32

what are the ordered pairs of 2pi?

Answer 32

( 1,0)

Question 33

what are the ordered pairs of pi/6?

Answer 33

(“root 3”/2, 1/2)

Question 34

what are the ordered pairs of pi/4?

Answer 34

(“root 2”/2, “root 2”/2)

Question 35

what are the ordered pairs of pi/3?

Answer 35

(1/2, “root 3”/2)

Question 36

what are the ordered pairs of pi/2?

Answer 36

(0,1)

Question 37

what are the ordered pairs of 2pi/3?

Answer 37

(-1/2, “root 3”/2)

Question 38

what are the ordered pairs of 3pi/4?

Answer 38

(“-root 2”/2, “root 2”/2)

Question 39

what are the ordered pairs of 5pi/6?

Answer 39

(“-root 3”/2, 1/2)

Question 40

what are the ordered pairs of pi?

Answer 40

(-1,0)

Question 41

what are the ordered pairs of 7pi/6?

Answer 41

(“-root 3”/2, -1/2)

Question 42

what are the ordered pairs of 5pi/4?

Answer 42

(“-root 2”/2, “-root 2”/2)

Question 43

what are the ordered pairs of 4pi/3?

Answer 43

(-1/2, “-root 3”/2)

Question 44

what are the ordered pairs of 3pi/2?

Answer 44

(0,-1)

Question 45

what are the ordered pairs of 5pi/3?

Answer 45

(1/2, “-root 3”/2)

Question 46

what are the ordered pairs of 7pi/4?

Answer 46

(“root 2”/2, “-root 2”/2)

Question 47

what are the ordered pairs of 11pi/6?

Answer 47

(“root 3”/2, -1/2)

Question 48

what is the quotient rule for finding derivative?

Answer 48

(u’v-uv’)/v^2