Unimodal function

Has one mode (usually a maximum, but could mean a minimum, depending on context). If f is defined on the interval $LaTeX: [a, b],$ let $LaTeX: x^*$ be its mode. Then, $LaTeX: f$ strictly increases from $LaTeX: a$ to $LaTeX: x^*$ and strictly decreases from $LaTeX: x^*$ to $LaTeX: b$ (reverse the monotonicity on each side of $LaTeX: x^*$ if the mode is a minimum). (For line search methods, like fibonacci, the mode could occur in an interval, $LaTeX: [a^*,b^*],$ where $LaTeX: f$ strictly increases from $LaTeX: a$ to $LaTeX: a^*,$ is constant (at its global max value) on $LaTeX: [a^*,b^*],$ then strictly decreases on $LaTeX: [b^*,b].$)