math flashcards !

differential equation

an equation that contains an unknown function and one or more of its derivatives

k?

constant of proportionality

slope field examples

ride the wave

on an increasing function, overestimate or underestimate

on a decreasing function, overestimate or underestimate

for trapezoid, over or underestimate

how to find the width of a rectangle ?

important formula fr

formulas for scary reimann sums

scary ah reimann formula

wow im scared

reimann example w scary formula

accumulation functions

know for the test please

maureen braun

maureen braun examples

know the properties of integrals

im warning u ….

fundamental theorem of calculus

fundamental theorem example

you dont need C yay

steps for u sub

find u

find the derivative of u (du)

plug things in

sub in for u at the end

add C if its not definite

if it is definite, use F(b)-F(a)

u sub definite integrals example

integration using long division example

integration using completing the square example

formula for completing the square

(b/2a)²

critical points on a graph

critical points are non-differentiable

critical points algebraically

candidates test example

first derivative test for relative extrema

intervals of concavity (second derivative test) example

big practice problem

steps for optimization problems

optimization practice

if something is outside the interval…

eliminate it!! it cannot be an answer

second derivative test technique 2

v(t) > 0 means

particle is moving up or to the right

v(t) < 0 means

particle is moving down or to the left

v(t) = 0 means

particle is not moving (at rest)

average velocity

change in position/change in time

speed

the absolute value of velocity (always positive)

if velocity and acceleration have the same sign

the particle is speeding up

if velocity and acceleration have different signs

the particle is slowing down

displacement

final position - initial position = change in position

can be negative or positive

distance

always positive value

if this is a velocity graph, how would you find the acceleration?

check slope of each part

positive slope = positive acceleration

when do this have the greatest speed?

speed = absolute value of velocity v(t)

so t = 0 and t = 2

to know if something is increasing…

check the sign of its first derivative

for example height is increasing if h’(t) is positive

strategy for related rates

reminder that….

you have to watch out for values that are constant and standing alone!!! their derivative is always zero

pi is always a constant and can stay 

what are linear approximations

the tangent line of a function at x=a can give you an approximate value of f(x) for points close to x=a

example of linear approximations

basically:

1. set up y-f(a)=f’(a)(x-a)

2. plug in everything you know about your original value

3. plug in your estimate value to x

4. solve for y

hospitals rule

use for 0/0 limits or if limits are going to ± infinity !!!!

you can keep trying hospitals until you get an answer 🙂

reminder that

you can have negative values for related rates

KNOW UR UNITS FOR RELATED RATES

how to describe double prime

practice problem

practice problem

practice problem

related rates help

help 

two ways of writing inverse trig functions

arc__ and __^-1x

make sure you know the trig functions by heart

inverse trig unit circle

quick refresher

a general rule is to find

derivatives of a general function FIRST, then plug in values.

practice

practice

reminder

horizontal/vertical lines

derivatives for trig

practice

practice

what is differentation

the process of finding a derivative

instantaneous rate of change

u2 notes

2.1

2.2

2.2

2.3

2.3

2.3

what values of a and b would make the function differentiable at the given value of x (2.3)

2.3

2.4

2.4

REMINDER

-simplify first especially for trig stuff

2.5

2.5

rememeber

dont flip the difference quotient up

review

2sinxcosx=

sin2x