Calc Mid term
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how does the number of primes affect differentation?
number of primes = number of times we differentiate

f(x) =x^53x^3+8x^25x+10
find f'(x)
5x^49x^2+16x5

f''(x) > f(x)=x^53x^3+8x^25x+10
5(4x^3)9(2x)+16 > 20x^318x+16

f'''(x) >x^53x^3+8x^25x+10
60x^218

F''''(x) > x^53x^3+8x^25x+10
60(2x) > 120x

4 Step Method for solving derivative
 1. F(x+h) > replace all x in function w/(x+h)
 2. f(x+h)f(x) > subtract the original function
 3. f(h+h)f(x)/h > divide by h
 4. take limit > plug in 0 for all h

in terms of demand & supply, when is the equilibrium graphically?
where the demand curve and supply curve intersect

how do you find equilibrium?
add the equations of the supply & demand & solve when = to 0

Break even point
BreakEven Point = FixedCosts/(1VariableCosts/Sales

how do you find a limit?
plug in numbers approaching the limit defined by the function.

domain:
possible numbers that can make sense for the solution

informal definition of limit
plugging a series of numbers in close to the limit as trial/error.

how do you graphically tell where the limit is?
where the 'hole' in the graph is

how to find limit
plug in the limit into the function

what does lim/x>0+ =1 mean?
as the right hand limit approaches 0, 1 is the closest it can get

lim/x>a=l only if?
lim/x>a+ AND limt/x>a

a function is not graphically continuous when?
you are not able to complete the graph without lifting the pencil

a function is continuous if?
 1. f(a) is defined
 2. lim/x>a exists
 3. lim/x>a=f(a)

formal definition fo continuity
 A function f is continuous at x = x0 if
 exists and is f(x0).

formula for average rate of change
f(b)f(a)/ba

what relation does the slop of the secant line have to the rate of change?
quantity increases at the rate of the value of m

limit definition of derivative:
f(x+h)f(x)/h

f'(a) representa what of the tangent line?
the slope

what is the difference between avg rate of change & instantaneous rate of change?
instant = specific point of change, avg = general change

1. what is the rate of change of f(x) when x=a?
2. at what rate is f(x) growing/increasing/decreasing/changing when x=a
3. how is f(x) fast/quickly grow/increas/decreas/chang when x=a
the same way of asking rate of change