Consider the following function.

$f(x)=4x^{3}21x^2-294x7$

$($a$)$ Find the intervals on which $f$ is increasing. $($Enter your answer using interval notation.$)$

Amazing workt

Find the interval on which $f$ is decreasing. $($Enter your answer using interval notation.$)$

$$

Check the plus and minus signs of all terms and$/$or values.

$($b$)$ Find the local minimum and maximum values of $f.$

local minimum value $$

local maximum value $$

$($c$)$ Find the inflection point.

$(x,y)=()$