Chapter 3.3-3.5 Flashcards Preview

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Flashcards in Chapter 3.3-3.5 Deck (48)
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1

what is a derivative of a constant?

zero

2

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

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

3

what is the product rule?

d/dx (uv)= (u'v+uv')

4

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

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

5

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

1. f''(x)
2. d^2y/dx
3. y''

6

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

it is just zero

7

what does "find the horizontal tangent(s)" mean?

means find x when the derivative equation equals zero

8

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

slope is zero

9

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

y-y1 = m (x-x1)

10

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

this is a maximum or minimum of the original equation

11

what is the derivative of sinx?

cosx

12

what is the derivative of cosx?

-sinx

13

what is the derivative of tanx?

sec^2x

14

what is the derivative of cscx?

-cscx * cotx

15

what is the derivative of secx?

secx* tanx

16

what is the derivative of cotx?

-csc^2x

17

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

original equation

18

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

1st derivative

19

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

2nd derivative

20

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

3rd derivative

21

what is the equation for displacement?

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

22

what is the equation for average velocity?

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

23

what is the equation of speed?

it is just the absolute value of the velocity equation

24

when velocity hits zero what does this mean?

means change in direction

25

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

negative velocity (negative slope)

26

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

positive velocity (positive slope)

27

how do you know if a particle is standing still?

when velocity is zero

28

how do you know if a particle is speeding up?

velocity and acceleration have the same sign

29

how do you know if a particle is slowing down?

velocity and acceleration have different signs

30

cosx is the value of ...

the x coordinate