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AP CALCULUS AB
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Gravity
Terms in this set (39)
Trig Identities
dy/dx
Intermediate Value Theorem
Extreme Value Theorem
There must be a max and min if the function is continuous on [a,b]
Linear Approximation
F(x)~=~f(a) +f`(a)(x-a)
Finding Average Velocity
Numerical Differentiation
Used to estimate the derivative
(F(x+h)-f(x))/h
Inflection Points
To find inflection points
1. Find the second derivative
2. Set the second derivative equal to zero
3. Solve for x
Optional
4. Plug in and solve for f(x)
Mean Value Theorem
F(x): Increasing or Decreasing
If f`is positive, then f(x) is increasing
If f` is negative, then f(x) is decreasing
F(x): Concavity
If f`` is positive, then f` is increasing, and the concavity of f(x) is upwards
If f`` is negative, then f` is decreasing, and the concavity of f(x) is downwards
Absolute Max./Min.
Only occur at critical points or end points of a continuous function (guaranteed by the EVT)
Differentiation: Product Rule
Differentiation: Quotient Rule
Differentiation: Chain Rule
Differentiation: Inverse Functions
Differentiation: Implicit Functions
Differentiation: Power Rule
Differentiation: Logarithms
d/dx of ln|x| = 1/x
d/dx of log base a of |x| = 1/(ln(a)x)
d/dx of ln|f(x)| = f`(x)/f(x)
Differentiation: Trig Functions
Related Rates
Suppose two variables, each a function of "time", are related by an equation.
1. Differentiate both sides of the equation
2. Use data given for variables and on of the rates to solve for the other rate
Optimization with Constraint
1. Visualize the problem; name the variables
2. Write down the objective function - the one to be optimized - as a function of two variables
3. Write down a Constraint Equation relating the variables
4. Use the constraint to rewrite the objective function in terms of one variable (Isolate one of the variables and then plug in for that variable)
5. Analyze the new function of one variable to find its optimal point(s) and the optimal value
Indefinite Integral
Definite Integral
Fundamental Theorem of Calculus
Second Fundamental Theorem of Calculus
MVT for Integrals
Integration: Power Rule
Integration: Natural Logarithm
(squiggly line antiderivative)d/du = ln|u| + C
Integration: Exponential Function
Integration: Trig Functions
http://calculus.nipissingu.ca/tutorials/integralgifs/int_indef_trigtable.gif
Area Between Curves
Volumes of Solids of Revolution
Rotating the the region between two curves about a line, then finding the volume created
Disk Volume
Washer Volume along x axis
Washer Volume along y axis
Same as along the x axis simply replace x with y (replace every single x with a y)
Cylindrical Shell Volume
h = R-r
Riemann Sum
Riemann Sum: Trapazoidal
http://images.slideplayer.com/22/6418662/slides/slide_4.jpg
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