# Exercici 07.8

kill(all)$

a)

f1(x):=(abs(x))^3;

wxplot2d([f1(x)], [x,-2,2])$

f11(x):=x^3;
f12(x):=-x^3;

Df11(x)=diff(f11(x), x);
Df12(x)=diff(f12(x), x);

'(D+f1(0))=limit((f11(x)-f11(0))/(x-0), x, 0, plus);
'(D-f1(0))=limit((f12(x)-f12(0))/(x-0), x, 0, minus);

diff(f1(x),x);

ratsimp(%);

Df1(x):=3*x*abs(x);

wxplot2d([Df1(x)], [x,-2,2])$

diff(Df1(x),x);

ratsimp(%);

D2f1(x):=6*abs(x);

wxplot2d([D2f1(x)], [x,-2,2])$

diff(D2f1(x),x);

D3f1(x):=(6*x)/abs(x);

wxplot2d([D3f1(x)], [x,-2,2])$