Given $f(x)=4x^3+6x^2-72x+3.$ Let's find the absolute minimum and absolute maximum values of $f$ on the interval $-6,3.$

Part a$)$ Find the critical numbers of $f.$ Enter your answers as a comma separated list.

$x=$

$$

Part b$)$ What are the input values that we must use to determine the absolute minimum and absolute maximum values of $f?$ Enter your answers as a comma separated list.

$x=$

$$

Part c$)$ What are the absolute minimum and absolute maximum values of $f$ on the interval $-6,3?$

the absolute minimum value of $f$ is $$ and

the absolute maximum value of $f$ is $$