Extremum of the function online calculator

Maximum of minimum point of the function called extremum. Look at the picture of some function:

sample of function with minimum and maximum

From the plot, one can conclude that the points (x1, y1), (x3, y3) are maxima of the function. The points (x2, y2), (x4, y4) are minima of the function. Both, these points are called extrema of the function.

The tangent of the function is extrema points is parallel to the abscissa axis (geometric sense). Hence, the derivative of the function equals to zero at extrema points (requirement of the extrema). In addition, derivative may not exist in extrema points.

Sometimes, we need to find minimal (maximal) value of the function at some interval [a, b]. In this case, one need to find all the extrema points which belongs to this intervals and also check the values of the function at the borders of the interval.

Choose expression input type:

Expression input type:

Set options to find function's extremum:

Choose stationary point type: .

Function's variable

search for function's extremum on the given interval [ ; ]

Function to calculate the extremum

Input function which extremum you want to find:

Other useful links:

Step by step indefinite integral solution sample
Basic feature of indefinite integral