minimum

(noun)

The smallest value of a set.

Related Terms

Examples of minimum in the following topics:

  • Relative Minima and Maxima

    • The local minimum is the y-coordinate $x=-1$which is $-2$.
    • The absolute minimum is the y-coordinate which is $-10$.
    • This curve shows a relative minimum at $(-1,-2)$ and relative maximum at $(1,2)$.
    • The local minimum is at the $y$-value of−16 and it occurs when $x=2$.
    • This graph has examples of all four possibilities: relative (local) maximum and minimum, and global maximum and minimum.

  • Applications of Hyperbolas

    • This is associated with the particle's total energy E being less than the minimum energy required to escape, and so E is said to be negative in these cases.
    • However, this is the very special case when the total energy E is exactly the minimum escape energy, so E in this case is considered to be zero.
    • If there is any additional energy on top of the minimum (zero) value, the trajectory will become hyperbolic, and so E is positive in the hyperbolic orbit case.

  • Financial Applications of Quadratic Functions

    • The method of graphing a function to determine general properties can be used to solve financial problems.Given the algebraic equation for a quadratic function, one can calculate any point on the function, including critical values like minimum/maximum and x- and y-intercepts.

  • What is a Quadratic Function?

    • where $h$ and $k$ are respectively the coordinates of the vertex, the point at which the function reaches either its maximum (if $a$ is negative) or minimum (if $a$ is positive).

  • Application of Systems of Inequalities: Linear Programming

    • This occurs when the resulting value of the entering variable is at a minimum.
    • If the pivot column is c, then the pivot row r is chosen so that $b_{r}/a_{cr}$ is at a minimum.
    • Of these, the minimum is 5, so row 3 must be the pivot row.

  • Graphing Equations

    • Parabolas can open up or down, right or left; they also have a maximum or minimum value.

  • Parts of a Parabola

    • If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function.

  • Ellipses

    • The distance between antipodal points on the ellipse, or pairs of points whose midpoint is at the center of the ellipse, is maximum along the major axis or transverse diameter, and a minimum along the perpendicular minor axis or conjugate diameter.

  • Parallel and Perpendicular Lines

    • Every point on $f(x)$ is located at exactly the same minimum distance from $g(x)$.

  • The Rule of Signs

    • The minimum number of complex roots is equal to: