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concavity occurs at
points of inflection
critical point
where the slope changes from positive to negative
points of inflection of f’(x)
are the zeros of f”(x)
function f(x) increases
where f’(x) is above the x axis
f’’(x) is positive where
the slope of f’(x) is positive
f(x) is concave up
when f’(x) has a positive slope
f(x) is concave down
when f’(x) has a negative slope
an x intercept on f’(x) is
a min/ma/POI on f(x)
when the curve on f’(x) is below the x axis
f(x) is decreasing
when the curve on f’(x) is above the x axis
f(x) is increasing
when f’(x) goes from above the x axis to below
on f(x) its a max
when f’(x) goes from below the a axis to above
on f(x) its a max
