Let [math]

Input the interval(s) on which [math] is increasing.

Input the interval(s) on which [math] is decreasing.

Find the point(s) at which [math] achieves a local maximum.

Find the point(s) at which [math] achieves a local minimum.

Find the intervals on which [math] is concave up.

Find the intervals on which [math] is concave down.

Find all inflection points.