Use the derivative $$ f^{\prime}(x)=x^{2}(x-2)(x+2) $$ to determine the local maxima and minima of $$ f $$ and the intervals of increase and decrease, Sketch a possible graph of $$ f(f $$ is not unique).

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Mills Simpson · Accepted Answer

The critical points are $$ x = -2, 0, 2 $$. The function increases on $$ (-\infty, -2) $$ and $$ (2, \infty) $$, and decreases on $$ (-2, 0) $$ and $$ (0, 2) $$. There is a local maximum at $$ x = -2 $$ and a local minimum at $$ x = 2 $$.

Use the derivative \( f^{\prime}(x)=x^{2}(x-2)(x+2) \) to determine the local maxima and minima of \( f \) and the intervals of increase and decrease, Sketch a possible graph of \( f(f \) is not unique).

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Use the derivative \( f^{\prime}(x)=x^{2}(x-2)(x+2) \) to determine the local maxima and minima of \( f \) and the intervals of increase and decrease, Sketch a possible graph of \( f(f \) is not unique).

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