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Instantaneous Rate of Change
Slope
lim f(x1+delta x)-f(x1)/delta x
average rate of change: delta y/delta x
instantaneous rate of change: lim (delta y/delta x)
Point
Jump
Infinite are undefined derivative because
f (c)= DNE
lim f(x)=L
Approach
Def: the function is contunues.
f(c) is defined
lim f(x) exists
Discontinuity:
jump
point
infinite
Constant K
Sum Rule
Difference Rule
Product Rule
Quotient Rule
Power Rule
Derivative of a Constant
Power Rule
Constant Multiple Rule
Sum/Difference Rule
Product Rule
Quotient Rule
Chain Rule
First derivative
Second derivative
x and y mixed together
To find dy/dx, take d/dx each side of equation, and simplify
Extreme Value
L'Hoptial's rule
Minima and maxima
Local Maxima: f(c) is an abs min for some open interval containing
Local Minima: f(c)is an abs max for same open interval containing
lim f(x)/g(x)=lim f'(x)/g'(x)
f and g are diff'able functions and
f(a)=g(a)=0
Method of retrieving function from wihch a given derivative came
Trigonometric
Use substitution
Separate Sine or cosine
Integrate with Substitution
Area between two curves
Volumes of revolution
Cylindrical shells