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f(x) increasing
f prime positive
f(x) decreasing
f prime negative
f(x) flat points (f(x) = 0 at that one point)
f prime hits the x axis
f(x) local max
f prime crosses from positive to negative
f(x) local min
f prime crosses from negative to positive
f(x) concave up to concave down
f prime local max
f(x) concave down to concave up
f prime local min
f(x) concave up
f prime is increasing
f(x) concave down
f prime is decreasing
f(x) vertical tangent , slope goes to infinity
f prime undefined and like vertical asymptote
f(x) = constant
f prime slope y= zero for the interval
f(x) very steep increasing
large positive f’
f’ very steep decreasing
large negative f’
f(x) steepness flat
f’ near 0
f(x) sharp points
f prime break or jump
f(x) hole
f prime hole
f(x) had a local max OR min at x=a and is smooth
f prime of a equals 0
Even function g(-x)=g(x)
g’(-x) = -g’(x) even function
Odd function g(-x)=-g(x)
Odd function g’(-x)=g’(x)