For the function below, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing. $$ f(x)=8 x^{3}-90 x^{2}-96 x+6 $$ (a) Find the critical number(s). First, find $$ f^{\prime}(x) $$. $$ f^{\prime}(x)=24 x^{2}-180 x-96 $$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The critical number(s) is/are (Use a comma to separate answers as needed.) There are no critical numbers.

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Estrada O'Quinn · Accepted Answer

The critical numbers are $$ x = -\frac{1}{2} $$ and $$ x = 8 $$.

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