Sketch the curve y=x^3+(3/2)*x^2-6*x+4, indicating all relative extreme points and inflection points.
y[x_]:=x^3+(3/2)*x^2-6*x+4
y1[x_]=D[y[x],x]
y2[x_]=D[y1[x],x]
{x,y[x]}/.Solve[y1[x]==0,x]
{x,y[x]}/.Solve[y2[x]==0,x]
Plot[y[x],{x,-4,2.6},AxesLabel->{x,y}]
Local maximum at: {x,y}={-12,14}
Local minimum at: {x,y}={1,1/2}
Inflection at: {x,y}={-1/2,29/4}