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Find points of inflection, concavity, and sketch graph of function.

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1. For the function
a. Find all the points of inflection of
b. Determine the concavity of each part of the graph, showing your results in a table.
c. Sketch the graph on a suitable scale showing the concavity and points of inflection.

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Points of inflection, concavity, and graphs are investigated. The solution is detailed and well presented.

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1. For the function
a. Find all the points of inflection of
f'(x) = 4x3 - 12x2 + 16 = 0
or x3 - 3x2 + 4 = 0
By observation, x = -1 is a solution of the above equation, therefore, (x + 1) should be factor.
x3 - 3x2 + 4 = ...

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