What is Bisection, secant and Brent’s methods?

The bisection method halves a bracket $[a, b]$ with $f(a)f(b) < 0$ at each step. The secant method replaces the derivative in Newton’s method by the slope through the last two iterates. Brent’s method (Brent, 1973) keeps a bracket and takes an inverse quadratic interpolation or secant step when it stays inside the bracket and shrinks it fast enough, and a bisection step otherwise.