Question 870676: Determine the coordinates (x,y) of the turning point of the curve y=x lnx - 2x, and decide if is a maximum or minimum point.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Determine the coordinates (x,y) of the turning point of the curve y=x lnx - 2x, and decide if is a maximum or minimum point.
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To find the turning point, take the 1st derivative and set=0:
y' = dy/dx = 0 = ln(x) + x/x - 2 = ln(x) + 1 - 2 = ln(x) - 1
So ln(x) = 1 -> x = e^1 = 2.7182818...
To determine whether the point is a maximum or minimum, check the sign of the 2nd derivative at the inflection point:
y'' = 1/x = 1/e (positive)
So the point is a minimum.
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