Standard 13: Conceptual Underpinnings of Calculus
In grades 912, the mathematics curriculum should include the informal
exploration of calculus concepts from both a graphical and a numerical
perspective so that students can:

Determine maximum and minimum points of a graph and interpret the results
in problem situations
Benchmarks 9C (The Mathematical World: Shapes)
Grades 68, page 219
Graphs can show a variety of possible relationships between two variables.
As one variable increases uniformly, the other may do one of the following:
always keeps the same proportion to the first, increase or decrease steadily,
increase or decrease faster and faster, get closer and closer to some limiting
value, reach some intermediate maximum or minimum, alternately increase
and decrease indefinitely, increase or decrease in steps, or do something
different from any of these.

Investigate limiting processes by examining infinite sequences and series
and areas under curves
and so that, in addition, collegeintending students can:
Understand the conceptual foundations of limit, the area under a curve,
the rate of change, and the slope of a tangent line, and their applications
in other disciplines
Analyze the graphs of polynomial, rational, radical, and transcendental
functions