unit 2 test Flashcards

1
Q

FIND HOW TO FIND DERIVATIVE OF GRAPH

For example f’(2)

A

Use slope

Find slope on graph at f(2)
Then find derivative if while function(use rules)
Then plug in value if x which is 2 into f(x) and value of g’(x) which si the slope for f’(x)

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2
Q

velocity moves which directions

which positive which negative

A

left to right

left negative right post i’ve

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3
Q

acceleration moves which directions

which positive which negative

A

up down

increasing decreasing

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4
Q

the speed of a particle is increasing or accelerating if

A

the velocity and acceleration have the same sign

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5
Q

what is speed

A

the absolute value of velocity

always positive

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6
Q

find all t for which the particle is moving right

A

find derivative of position function to find velocity

solve for t

turn the solutions into intervals

ex. t= 0, t= 3

interval [0,3) (3,infinity)

then choose a pt in interval and plug into v(t)
see if positive or negative (positive means moving it the right)

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7
Q

when to use brackets

A

if greater than ir equal to

AKA ENDPOINT

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8
Q

always use parentheses for

A

infinity

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9
Q

find all t for velocity increasing

means find the…

A

acceleration

do same as (find particle movin to right) velocity

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10
Q

find all t for which speed of particle is increasing justify

check if v(t) and a(t) are same sign

A

plug in number for v(t) and for a(t) if some sign then the particle is increasing

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11
Q

circumference of a circle

A

pi (d)

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12
Q

area if a circle

A

(pi)r^2

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13
Q

diameter of circle

A

2r

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14
Q

solving related rate problems

A

write down given, find, and equation

draw diagram if needed!

the rate given is the given

you are trying to find dR/dt when BLANK

equation is based on shape in word problem

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15
Q

what to differentiate related rates

A

any rate that cna chnage in the word problem/equation

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16
Q

when doing related rates write down

A

given
find
equation

17
Q

what does the given have

A

the rate listed in the word problem with respect to time

18
Q

área circle

A

pi(r)^2

19
Q

are triangle

A

1/2bh

20
Q

área rectangle

A

l(w)

21
Q

área square

A

s^2

22
Q

área trapezoid

A

b1+b2/2

23
Q

volume cylinder

A

pi(r)^2(h)

24
Q

volume cone

A

1/3pi(r)^2h

25
Q

what to look out for related rates with triangles

A

similar triangles
SOC CAH TOA
pythagorean theorem

26
Q

Find the instantáneous rate of change of f’ means

A

Find the derivative if f’
AKA
Find f’’

27
Q

Units for f’’ in millimeters

A

Minutes per milliliter per milliliter

28
Q

Instantaneous rate of change

A

Find derivative

29
Q

Find derivative on graph at certain point

A

Equal to finding the slope at that certain point

30
Q

For what value is the object at rest

A

Find position function or f’(x) or s’(t)

31
Q

When finding the average on an interval
Velocity for example, use what function

Acceleration for example use what function?

A

Position function

Velcoty function

32
Q

In lhopsitals rule you don’t use what rule

A

Quotient rule

33
Q

How to: find instantaneous rate if change at (1,1) for x+2y -y =2

A

Find derivative then plug in values into derivative but like average rate of change

f(b)-f(a)/b-a

34
Q

Go through AB CALCULUS OATH TO A 5 PROBLEMS

A

DO IT NOWWW

35
Q

inverse of g’(x) is

A

1/f’(g(x)