Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=-4x^2-40x-23$

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

$($Type integers or simplified fractions.$)$

A$.$ The function has a local minimum $fl=,$ and no local maximum.

B$.$ The function has a local maximum $f=$ and a local minimum $f=$

C$.$ The function has a local maximum $f||=77,$ and no local minimum.

D$.$ The function has no local extrema.