An Inflection Point is where a curve changes from Concave upward to Concave downward (or vice versa) ... And the inflection point is where it goes from concave upward to concave downward (or vice versa). To find a point of inflection, you need to work out where the function changes concavity. If the sign does not change, then there exists no inflection point. "Calculus-based reasoning" with the second derivative of a function can be used to justify claims about the concavity of the original function and about its inflection points. If the sign of the second derivative changes as you pass through the candidate inflection point, then there exists an inflection point. If you can pinpoint … Check if the second derivative changes sign at the candidate point. That is, where it changes from concave up to concave down or from concave down to … Let's work out the second derivative: Example: y = 5x 3 + 2x 2 − 3x. If y'' is continuous and you can show that in one dorection y'' > 0 and in the other direction y", 0, then somewhere in between y'' must equal zero. Inflection Points .
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