Problem 53E

53. If $f(x)=2 x^{2}-x^{3}$, find $f^{\prime}(x), f^{\prime \prime}(x), f^{\prime \prime \prime}(x)$, and $f^{(4)}(x)$.

Graph $f, f^{\prime}, f^{\prime \prime}$, and $f^{\prime \prime \prime}$ on a common screen. Are the graphs consistent with the geometric interpretations of these derivatives?

 

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