How do you find points of inflection on a graph of f'

  find the extrema of f'

Step-by-step explanation:

Points of inflection on a graph of f(x) are where the concavity changes from up to down, or vice versa. These are points where the second derivative is zero. On a graph of the first derivative, f'(x), those will be points where the slope of f'(x) is zero: extreme points (maxima or minima).

The slope of f'(x) may also be zero at a flat spot, but that will not be a point of inflection of f(x), because the sign of the slope does not change there.

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By way of illustration, we show a graph of f' (red) and the corresponding function f(x) (dashed green). The marked points are where the slope of f' is zero. Only the right-most of those represents a point of inflection of f(x).