Analyze and sketch each function using the algorithm for curve sketching. $[14$ marks$]$

$k(x)=\frac{1}{4}{x}^4-\frac{9}{2}{x}^2$

Intercepts: $q,$

$[2]$

Determine & Verify Extremas: $[3]$

Determine and Verify Inflection Points: $[3]$

Intervals of Increase$/$Decrease $[2]$

Intervals of Concavity $[2]$

Sketch $[2]$