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Soccerboy496
Soccerboy496 asked in Science & MathematicsMathematics · 8 years ago

Please Help! DON'T UNDERSTAND!!!?

"Use the second derivative and a sign diagram to determine the intervals on which the graph of f(x)= x^2 + Ln(x) is concave upward or concave downward (use interval notation) and state the point of inflection (x,y) (you may approximate to the nearest hundredth if desired). Keep in mind that the domain of f is (0,infinity)"

Thanks for the help!! Will give out points!!

Update:

what do you mean "x". It's the equation! Thanks!

Update 2:

The only critical number is 0? Is that right?

And there is no point of inflection. correct?

Thanks!

2 Answers

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  • James
    Lv 5
    8 years ago
    Favorite Answer

    y = x^2 + ln(x)

    y' = 2x + 1/x

    y" = 2 - 1/x^2

    range is 0 to infinity because ln(<0) DNE. Inflection points exist when y" = 0. So:

    0 = 2 - 1/x^2

    0 = 2x^2 - 1

    1/2 = x^2

    x = +/- sqrt(1/2)

    So, evaluate the function between 0 and sqrt(1/2). Then evaluate between sqrt(1/2) and infinity.

  • Anonymous
    8 years ago

    what do you mean "x"?

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