Método de Posição Falsa

\(l: \quad \left(\begin{array}{c} x(t)\\y(t) \end{array}\right)=\) \(\left(\begin{array}{c} a\\f(a) \end{array}\right) +t\) \(\left(\begin{array}{c} b-a\\f(b)-f(a) \end{array}\right)=\)
\((1-t)\left(\begin{array}{c} a\\f(a) \end{array}\right)+t\) \(\left(\begin{array}{c} b\\f(b) \end{array}\right)\)

1. Intersecção entre \(l\) e o eixo \(x\) , \(t=t_0\) :

   \(y(t_0)=0 \quad \Leftrightarrow \quad t_0=-\frac{f(a)}{f(b)-f(a)} \Rightarrow 1-t_0=\frac{f(b)}{f(b)-f(a)}\)

2. \(\Rightarrow \quad x(t_0)=\frac{ af(b)-bf(a) }{ f(b)-f(a) }\)