QUESTION $41$ POINT

Using the First Derivative Test, what are the local extrema for the function $s(x)=-\frac{4}{3}{x}^{3}24x^2-140x-15?$

Select the correct answer below:

There is a local minimum at $x=6.$

There is a local minimum at $x=5$ and a local minimum at $x=7.$

There is a local maximum at $x=6.$

There is a local maximum at $x=5$ and a local maximum at $x=7.$

There is a local minimum at $x=5$ and a local maximum at $x=7.$

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