Given the function $f(x)=5x^7-84x^6,$ find $f^{\text{'}}(x),$ classify the critical numbers, and identify the intervals of increase and decrease for the function.

$f^{\text{'}}(x)=$

The smaller of the critical numbers is $x=$

It is a Local Maximum $$

The larger of the critical numbers is $x=$

It is

The interval over which $f(x)$ is increasing is

The interval over which $f(x)$ is decreasing is