How do you find the local maxima/ local minima of a polynomial function by hand?

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For f(x),
local maxima occur where f '(x) = 0 and f ''(x) < 0 and
local minima occur where f '(x) = 0 and f ''(x) > 0
If f ''(x) = 0, you'll need to test points on each side of x....Show more

set up a table with 2 columns, one for x values and one for y values. pick the x values and calculate the y values, entering into each and each contained in the table. Then plot the factors on graph paper. you should apply a scale ingredient for cubic or quartics, because the values have a tendency to improve quickly. Factoring or differentiating the needs, in case you may, will supply clues on what x values to pick on....Show more