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) -> f(x)=x^5-3x^3+8x^2-5x+10
5(4x^3)-9(2x)+16 -> 20x^3-18x+16
F''''(x) -> x^5-3x^3+8x^2-5x+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
Break-Even Point = FixedCosts/(1-VariableCosts/Sales
how do you find a limit?
plug in numbers approaching the limit defined by the function.
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
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'(a) representa what of the tangent line?
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
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