# Ejercicio 07.4

## Apartado a)

kill(all)$

f(x):=3*x^4 + 4*x^3 -12*x^2 + 20;

diff(f(x), x);

Eq1:12*x^3+12*x^2-24*x=0;   solve(Eq1, x);

x1:1$       P1=[x1, f(x1)];
x2:-2$      P2=[x2, f(x2)];
x3:0$       P3=[x3, f(x3)];

wxplot2d([f(x)], [x,-3,2], [gnuplot_preamble, "set grid;"])$

## Apartado b)

kill(all)$

f(x):=(x - 1)^(2/3);

diff(f(x), x);

Df(x):=2/(3*(x-1)^(1/3));

x0=x0:9;
y0=y0:f(x0);        
m=m:Df(x0);

y - y0 = m*(x - x0);

expand(%);

yT(x):=(x/3) + 1;

y - y0 = (-1/m) * (x - x0);

expand(%);

yN(x):=31 - 3*x;