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# Math Problem Easy, PLLeeeaasse?

f(x) = x^4-2x^3

Find all relative extrema and points of inflection

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- Anonymous1 decade agoFavorite Answer
The extrema will occur when the derivative is zero. So solve for x in

4x^3-6x^2 = 0

x^2*(4x-6) = 0 --> x = 0 or 3/2 could the x-coordinates of the extrema. BUT at x=0, it is not an extrema, it is only flat. So only at x=3/2 is it an extrema.

Points of inflection can be the extrema of the derivative, or aka, where the double-derivative of the function is 0. So solve for x in:

12x^2-12x = 0

12x*(x-1) = x --> x = 0 or 1 are the x-coordinates of the points of inflection. Both these points are valid

Source(s): math

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