= Solution
The <secant method> starts from two approximations $x_0,x_1$. Replace the <function> near its <zero of a function> by the <secant line> through $(x_{k-1},f(x_{k-1}))$ and $(x_k,f(x_k))$; the zero of that line is the next approximation:
$$
\boxed{x_{k+1}=x_k-f(x_k)\frac{x_k-x_{k-1}}{f(x_k)-f(x_{k-1})}.}
$$
Stop immediately if $f(x_k)=0$; otherwise the denominator must be nonzero. Each further step needs one new <function> evaluation and no <derivative>. There is no automatic bracketing or global <convergence> guarantee.<NIST Digital Library of Mathematical Functions/3.8 Nonlinear Equations>[§3.8(iii), Secant Method and equation 3.8.6]{ref}
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