The math word "curve" is referenced in the pages listed below.
This page explores one application of derivatives - analyzing the behavior of curves that represent functions in calculus. Interactive calculus applet.
Explores global extrema. This is just like the case for local extrema, except you need to find which one is biggest/smallest, and you may have to check endpoints. Interactive calculus applet.
Explores some special cases in curve analysis in calculus. Interactive calculus applet.
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