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calculus

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f(x)= −x2lnx
find the critical points , increasing & decreasing interval and concavity.Please just show me the steps on how to get the increasing and decreasing interval and critical pts . Thanks :)

  • calculus -

    Just use your derivatives.

    f = x^2 lnx
    f' = 2x*lnx + x^2 * 1/x = x(2lnx + 1)
    f' = 2lnx + 2x*1/x + 1 = 2lnx + 3

    Now, f is increasing when f' > 0
    f is concave up when f'' > 0
    max/min is where f' = 0 and f'' =/= 0
    inflection where f'' = 0

    Go for it!

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