[Solution] Consider the function f(x)=fracx^2x-2. (4 pts) Find the values of x such that f^prime(x)=0. (4 pts) Determine the intervals on which f^prime(x)>0
Question: Consider the function \(f(x)=\frac{x^{2}}{x-2}\).
- (4 pts) Find the values of \(x\) such that \(f^{\prime}(x)=0\).
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(4 pts) Determine the intervals on which \(f^{\prime}(x)>0\) and the intervals on which \(f^{\prime}(x)<0\)
(xc) (4 pts) Find the intervals on which \(f(x)\) is increasing and the intervals on which \(f(x)\) is decreasing. Determine the local minima and/or maxima, if any. Justify your answers.
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