Point of inflection full

Point of Inflection
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1. Point of inflection

2. What is the point of inflection An  inflection point  is the  point  where the concavity changes. At the  inflection point , the curve might go from concave down (with a decreasing slope) to concave up(with an increasing slope). ... At the inflection point ,  the second derivative  changes from negative to positive, and must be zero.

3. GRAPH

4. We decide the concavity from the 2 nd derivative Mathematically IF the 2 nd derivative = 0 at that point ( point of inflection ) OR IF the 2 nd derivative changes its sign at that point so (2 nd derivative = 0)

5. f(x) = First derivative f’(x) = 3 2 nd derivative f’’(x) = 6x Now set the second derivative equal to zero and solve for "x" to find possible inflection points.  

6. 2 nd derivative = 0 6x = 0 x = 0