For y = f(x), the second derivative of f, provided that it exists, is:
f''(x) = d/dx f'(x)
Other notations for f''(x) are:
d2y/dx2 and y''
For the interval (a, b), if f'' > 0, then f is concave upward, and if f'' < 0, then f is concave downward.
An inflection point is a point on the graph where the concavity changes from upward to downward or downward to upward.
If (c, f(c)) is an inflection point of f, then c is a partition number for f''.
|f(x)||Above x-axis||Below x-axis||x-intercept||Vertical asymptote?|
|f'(x)||Increasing||Decreasing||Local extremum?||Local extremum?|
|f''(x)||Concave upwards||Concave downwards||Inflection point?||Inflection point?|
c = -4