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

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

Progress

1/28

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) optimization minimum or maximum problem critical point local minimum or maximum point of inflection point where concavity of the graph changes where f"(x) = 0 y=e^i(x-a)^2 a shifts the graph left or right divide (x-a)^2 by b and b makes the graph wider or narrower y=a(1-e^-bx) 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 Revenue price x quantity Profit Revenue - cost usually written as pi Marginal Cost C'(q) Marginal Revenue R'(q) 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 sketches 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 b-a/n 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 distance 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 antiderivative working backwards from the derivative