### Standard 13: Conceptual Underpinnings of Calculus

In grades 9-12, 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 6-8, 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, college-intending 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