Método da Secante (1 passo)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
secante
About this calculator
The Secant Method calculator performs one iteration of the numerical method for finding roots of functions. Given two initial points x₀ and x₁, it computes x₂ using the formula: x₂ = x₁ − f(x₁)·(x₁−x₀)/(f(x₁)−f(x₀)). The secant method is an alternative to Newton-Raphson, as it does not require the derivative of the function, only function evaluations at the points. It is useful for continuous functions where the derivative is difficult or expensive to obtain.
How it works: you enter the function f(x), initial values x₀ and x₁, and the calculator returns x₂. The formula approximates the derivative by the difference of function values, generating a secant line that crosses the x-axis at x₂. This process can be repeated (iterated) until the root is found with desired accuracy. The calculator shows a single step, allowing you to proceed manually or understand the process.
When to use: in engineering, physics, and applied mathematics problems where zeros of nonlinear functions are needed. For example, to find the root of a polynomial or transcendental equation. It is especially useful when the function is complex and its derivative is not available. Cautions: the method may fail if f(x₁) = f(x₀) (division by zero) or if the initial points are poorly chosen, leading to divergence. Additionally, convergence is not guaranteed for all functions.
Frequently asked questions
How many iterations are needed to find the root?
The calculator performs only one step. The number of iterations depends on the function and desired accuracy; you may need to repeat the process several times.
What if the denominator is zero (f(x₁) = f(x₀))?
If f(x₁) equals f(x₀), the formula fails. Try choosing other initial values x₀ and x₁ that are closer to the root or that do not have the same function value.
Does the secant method always converge?
No. Convergence depends on the function and the choice of initial points. If the function is not continuous or the points are far from the root, the method may diverge.
What is the difference between the secant method and Newton-Raphson?
The secant method does not use the derivative, only two function evaluations per iteration, while Newton-Raphson uses the derivative. The convergence rate of secant is slightly lower (superlinear vs. quadratic).
Can I use the calculator for functions with multiple roots?
Yes, but the method may be less efficient or converge slowly. For multiple roots, modified methods are recommended.