find the extreme point(s) of the function f(x) = 0.25x^4 + 3x^3 - 18x^2 +10 and classify them

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find the extreme point(s) of the function f(x) = 0.25x^4 + 3x^3 - 18x^2 +10 and classify them

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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what do you mean by extreme points?
i think they mean extrema, maxima and minima, correct?
most likely, in that case differentiate and set equal to zero

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differentiate the equation. then use fishball method
f(x) = \[0.25x^4 + 3x^3 - 18x^2 +10\] Then differentiate f'(x) = \[x^3 + 9x^2 - 36x\]= \[x(x^2 + 9x - 36)\]= \[x(x+12)(x-3)\]
Then use fishball method -12 0 3 x - - - 0 + + + x+12 - 0 + + + + + x-3 - - - - - 0 + -------------------------------- - 0 + 0 - 0 + therefore, at x=-12 and x=3 there exists rel. min at x = 0, there exists rel max Hope I helped and I hope I did it right
yes i believe this is correct
Oh gosh thanks so much you guys this really helps

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