the point of inflection has a tangent with gradient = 0, ie. is a stationary point.
it occurs for x^3 graphs, where on both sides of the stationary point, y increases or decreases depending on the formula.
to test for this, we draw up a table and test for the number that results in f'(x) = 0, and then for a number higher than the x value that resulted in that, and lower than that.
the result will give us the shape of the graph
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