Study your flashcards anywhere!

Download the official Cram app for free >

  • Shuffle
    Toggle On
    Toggle Off
  • Alphabetize
    Toggle On
    Toggle Off
  • Front First
    Toggle On
    Toggle Off
  • Both Sides
    Toggle On
    Toggle Off
  • Read
    Toggle On
    Toggle Off

How to study your flashcards.

Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key

Up/Down arrow keys: Flip the card between the front and back.down keyup key

H key: Show hint (3rd side).h key

A key: Read text to speech.a key


Play button


Play button




Click to flip

28 Cards in this Set

  • Front
  • Back
L'Hopital's Rule
if the derivative is in intederminate form then use which is 0/0 and infinity/infinity
lim x->a f(x)/g(x) = lim x->a f'(x)/g'(x)
minimum or maximum problem
critical point
local minimum or maximum
point of inflection
point where concavity of the graph changes
where f"(x) = 0
a shifts the graph left or right
divide (x-a)^2 by b and b makes the graph wider or narrower
a is the asymptote and b is the stretch or shrink of the graph
y=a(x-h)^2 + k
a is stretch or shrink
h shifts right and left
b shifts up and down
global max and min
overall maximum and minimum
highest and lowest y values
substitute the cp into the f(x) set equal to zero to find y location on the graph to see which is the highest
price x quantity
Revenue - cost
usually written as pi
Marginal Cost
Marginal Revenue
maximum profit
Marginal Cost = Marginal revenue
R'(q) = c'(q)
on graph where space between is widest
Modeling Optimization problems
need two equations
the quantity needed to be optimized is the thing you want the derivative of
find the cp and ep to evaluate global max and min
cosh x
e^x + e^-x / 2
sinh x
e^x - e^-x / 2
d/dx cosh x
sinh x
d/dx sinh x
cosh x
hyperbolic functions to know
cosh(0) = 1
sinh(0) = 0
cosh(-x) = cosh x
sinh (-x) = -sinh x
cosh^2 x - sinh^2 x = 1
Extreme Value theorem
if f is continuous then must have a global max and global min on the closed interval
Mean Value theorem
f'(c) = f(b) - f(a) / b-a
delta t
n is the number of intervals and b and a is the interval
left and right increments
in a chart begin with the first value but don't take the last for the right hand value
begin with the second value and end with the last value for the left hand sum
average the two to find the most acurate measurement of the integral
sigma notation
definite integral
number at the top tells the number of intervals
number at the bottom tells where to begin
definite integral
integral from a to b f(t) dt
area under the curve
total change
definite integral
F(b) - F(a) = integral from b to a F'(t) dt
average value
1/b-a integral from b to a f(x) dx
working backwards from the derivative