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f(x)
the integral : area under curve from x to given point
f ‘ (x)
the expression in the integral: y value at given point
f ‘‘ (x)
the derivative of the expression in the integral: slope at given point
Inflection points when f ‘‘ (x)
changes in sign in terms of decreasing to increasing; from - to +, or + to -
Concave down when f ‘‘ (x) is
decreasing
concave up when f ‘‘ (x) is
increasing
Critical Points
at x values where y is zero
Rel min
when y value goes from - to +
Real Max
when y value goes from + to -