Aus Online Mathematik Brückenkurs 2
The function has zero derivative at three points,
x=a,
x=band
x=c
(see picture below), which are therefore the critical points of the function.
The point
x=b
is an inflexion point because the derivative is positive in a neighbourhood both the left and right.
At the left endpoint of the interval of definition and at
x=c, the function has local maximum points , because the function takes lower values at all points in the vicinity of these points. At the point
x=a
and the right endpoint, the function has local minimum points.
Also, we see that
x=c
is a global maximum (the function takes its largest value there) and the right endpoint is a global minimum.
Between the left endpoint and
x=a, as well as between
x=c
and the right endpoint, the function is strictly decreasing (the larger
x
is, the smaller
f
x
becomes), whilst the function is strictly increasing between
x=a
and x=c (the graph flattens out at
x=b, but it isn't constant there).
