maths

the curve c has equation y=x^2-1nx, x>0. Show that c has just 1 turning point and find its cordinates.

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asked by rita s
  1. 1 turning point means that y'=0 at only one place, and y"≠0 there

    y' = 2x-1/x
    y" = 2+1/x^2
    Note that y">0 for all x.

    y'=0 where
    2x^2-1 = 0
    x = ±1/√2
    But lnx is undefined for x<=0, so y'=0 only at 1/√2

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    posted by Steve

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