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Find the intervals on which f(x) = x^4 + 2x^3 − 36x^2 + 9x − 47...

Find the intervals on which f(x) = x^4 + 2x^3 − 36x^2 + 9x − 47 is concave down and up, along with the x-coordinates of any inflection points. Justify all your work.

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