Perform a first derivative test on the function $f(x)=4x^{5}10x^4-100x^{3}1$;$[-6,4]$

a$.$ Locate the critical points of the given function.

b$.$ Use the First Derivative Test to locate the local maximum and minimum values.

c$.$ Identify the absolute maximum and minimum values of the function on the given interval $($when they exist$)$

a$.$ Locate the critical points of f $.$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The critical point$($s$)$ is$($are$)$ at $x=$

$($Use a comma to separate answers as needed. Type an integer or a simplified fraction.$)$

B$.$ The function does not have a critical value.

b$.$ Locate the local maximum value. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

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

$($Type an integer or a simplified fraction.$)$

B$.$ There is no local maximum.

Locate the local minimum value. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

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

$($Type an integer or a simplified fraction.$)$

B$.$ There is no local minimum.

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