h=0.5;
x=0.5;

fxh=-0.1*(x+h)^4-0.15*(x+h)^3-0.5*(x+h)^2-0.25*(x+h)+1.2;
fx_h=-0.1*(x-h)^4-0.15*(x-h)^3-0.5*(x-h)^2-0.25*(x-h)+1.2;
dfdx_pt5=(fxh-fx_h)/(2*h)

h2=0.25;
fxh2=-0.1*(x+h2)^4-0.15*(x+h2)^3-0.5*(x+h2)^2-0.25*(x+h2)+1.2;
fx_h2=-0.1*(x-h2)^4-0.15*(x-h2)^3-0.5*(x-h2)^2-0.25*(x-h2)+1.2;
dfdx_pt25=(fxh2-fx_h2)/(2*h2)

dfdx=(4/3)*dfdx_pt25-(1/3)*dfdx_pt5