Let $f(x)=4x^3+6x^2-9x+12.$

Determine $f^{\text{'}}(x)$ and $f^{\text{'}\text{'}}(x).(4$ Points$)$

Determine the critical points $an\frac{d}{o}r$ inflection points. $(4$ Points$)$

Determine the intervals where $f(x)is$ strictly increasing and decreasing. $(4$ Points$)$

Determine the intervals where $f(x)is$ concave $u\frac{p}{c}$oncave down. $(4$ Points$)$

Use the above observations $to$ sketch $f(x).(4$ Points$)$