Finding Points of Inflection In Exercises15-36, find the points of inflection and discuss the concavity of the graph of the function.
To calculate: The points of inflection for the provided function and thus its concavity.
The function .
The inflection point of the function corresponds to the point where its second derivative disappears.
For a function f that is twice differentiable on an open interval I:
If for all x I n I, the function f is concave upwards on I and if for all x in I, the function f is concave downwards on I.
Now differentiate this twice,
Now equate the second derivative to zero to obtain,
Also, the second derivative does not exist when x takes the value 0.
Substitute this value in the function to obtain,
The inflection point divides this into three intervals
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