About Function Analysis Functions
Function Analysis Functions allow you to investigate and study expressions that you work with. The following analysis functions facilitate the mathematical analysis of other expressions.
• isContinuous(F,v,[x,y])—Returns 1 if the expression F with respect to the variable v is continuous over the interval, otherwise returns 0.
• discontPoints(F,v,[x,y])—Returns a vector of discontinuity points of the expression F with respect to the variable v. If the expression F is continuous over the interval, it returns the undefined value as a vector.
• localExtrema(F,v,[x,y])—Returns an Nx2 matrix of N local extremum points of F with respect to the variable v. Each pair represents a local extremum point and the expression value at that point.
• localMinima(F,v,[x,y])—Returns an Nx2 matrix of N local minimum points of F with respect to the variable v. Each pair represents a local minimum point and the expression value at that point.
• localMaxima(F,v,[x,y])—Returns an Nx2 matrix of N local maximum points of F with respect to the variable v. Each pair represents a local maximum point and the expression value at that point.
• globalExtrema(F,v,[x,y])—Returns an Nx2 matrix of N global extremum points of F with respect to the variable v. Each pair represents a global extremum point and the expression value at that point.
• globalMinima(F,v,[x,y])—Returns an Nx2 matrix of N global minimum points of F with respect to the variable v. Each pair represents a global minimum point and the expression value at that point.
• globalMaxima(F,v,[x,y])—Returns an Nx2 matrix of N global maximum points of F with respect to the variable v. Each pair represents a global maximum point and the expression value at that point.
Arguments
• F is any valid expression. You can type the expression directly as an argument or define it outside the function analysis function and type the name of F as an argument.
• v is a variable name.
• F and v are mandatory for all function analysis functions.
• x and y are real numbers that define an interval for which the analysis function displays its results. The interval can be any real number interval, from -∞ to +∞. Specifying an interval is optional.
• For isContinuous and discontPoints: If you do not specify an interval in the function arguments, the operation will be performed over the entire complex plane. If a real interval is specified, the operation will be restricted to that real interval only.
• For localExtrema, localMinima, localMaxima, globalExtrema, globalMinima, and globalMaxima: These functions operate over the real interval. If you do not specify an interval, the function defaults to the interval -∞ to +∞.
Additional Information
• The function analysis functions can be evaluated only using the symbolic evaluation operator.