Determine the point(s) on the curve y=frac{x^{2}}{ln x} where the tangent is horizontal.

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Accepted Answer

Step:1 ：Find the derivative of the function y = frac{x^2}{ln x}: frac{dy}{dx} = frac{2x}{ln x} - frac{x}{(ln x)^2}Step:2 ：Set the derivative equal to 0: frac{2x}{ln x} - frac{x}{(ln x)^2} = 0Step:3 ：Solve the equation for x: x = e^{frac{1}{2}}Step:4 ：Final Answer: The point(s) on the curve y=frac{x^{2}}{ln x} where the tangent is horizontal is at x = boxed{e^{frac{1}{2}}}

Answer

Step: 1 ：Find the derivative of the function y = frac{x^2}{ln x}: frac{dy}{dx} = frac{2x}{ln x} - frac{x}{(ln x)^2}Step: 2 ：Set the derivative equal to 0: frac{2x}{ln x} - frac{x}{(ln x)^2} = 0Step: 3 ：Solve the equation for x: x = e^{frac{1}{2}}Step: 4 ：Final Answer: The point(s) on the curve y=frac{x^{2}}{ln x} where the tangent is horizontal is at x = boxed{e^{frac{1}{2}}}

Determine the point(s) on the curve $y=\frac{x^{2}}{\ln x}$ where the tangent is horizontal.

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