Illustrate the construction of the secant method by means of a figure. When $f ^ { \prime } > 0$ on $I$, express $x _ { n + 1 }$ as a function of $x _ { n - 1 } , x _ { n }$ by means of the function $H _ { f }$ defined in question 3 of the third part.
(Recall: the secant method initializes with $x_0, x_1 \in I$, and at each step considers the line $L_n$ passing through $(x_{n-1}, f(x_{n-1}))$ and $(x_n, f(x_n))$, defining $x_{n+1}$ as the $x$-intercept of $L_n$.)