unit 2 test Flashcards
FIND HOW TO FIND DERIVATIVE OF GRAPH
For example f’(2)
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)
velocity moves which directions
which positive which negative
left to right
left negative right post i’ve
acceleration moves which directions
which positive which negative
up down
increasing decreasing
the speed of a particle is increasing or accelerating if
the velocity and acceleration have the same sign
what is speed
the absolute value of velocity
always positive
find all t for which the particle is moving right
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)
when to use brackets
if greater than ir equal to
AKA ENDPOINT
always use parentheses for
infinity
find all t for velocity increasing
means find the…
acceleration
do same as (find particle movin to right) velocity
find all t for which speed of particle is increasing justify
check if v(t) and a(t) are same sign
plug in number for v(t) and for a(t) if some sign then the particle is increasing
circumference of a circle
pi (d)
area if a circle
(pi)r^2
diameter of circle
2r
solving related rate problems
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
what to differentiate related rates
any rate that cna chnage in the word problem/equation
when doing related rates write down
given
find
equation
what does the given have
the rate listed in the word problem with respect to time
área circle
pi(r)^2
are triangle
1/2bh
área rectangle
l(w)
área square
s^2
área trapezoid
b1+b2/2
volume cylinder
pi(r)^2(h)
volume cone
1/3pi(r)^2h
what to look out for related rates with triangles
similar triangles
SOC CAH TOA
pythagorean theorem
Find the instantáneous rate of change of f’ means
Find the derivative if f’
AKA
Find f’’
Units for f’’ in millimeters
Minutes per milliliter per milliliter
Instantaneous rate of change
Find derivative
Find derivative on graph at certain point
Equal to finding the slope at that certain point
For what value is the object at rest
Find position function or f’(x) or s’(t)
When finding the average on an interval
Velocity for example, use what function
Acceleration for example use what function?
Position function
Velcoty function
In lhopsitals rule you don’t use what rule
Quotient rule
How to: find instantaneous rate if change at (1,1) for x+2y -y =2
Find derivative then plug in values into derivative but like average rate of change
f(b)-f(a)/b-a
Go through AB CALCULUS OATH TO A 5 PROBLEMS
DO IT NOWWW
inverse of g’(x) is
1/f’(g(x)
