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If f is increasing
f' > 0
If f is decreasing,
f' < 0
If f has a critical value at x=a,
f'(a) = 0 or DNE
If f has a MAX at x=a,
f'(a) = 0/DNE, and f' changes signs from pos to neg at x= a
If f has a MIN at x=a,
f'(a) = 0/DNE. and f' changes signs from neg to pos at x =a
If f is concave up,
f'' > 0
If f is concave down
f'' < 0
If f has a point of inflection at x=a
f''(a) = 0/DNE, and f'' changes signs at x = a
If f has a MAX at x=a,
f'(a) = 0/DNE, and f''(a) < 0
If f has a MIN at x=a
f'(a) = 0/DNE. and f''(a) > 0