Vase 1

The Marble and the Vase

A fairly common max/min problem asks the student to find the point on the parabola that is closest to the point .  The solution is not too difficult. The distance, L(x), between A and the point  on the parabola  is given by And the minimum distance can be found when This occurs when . The local…

Red Graph: $latex y={{x}^{3}}-4{{x}^{2}}+3x+4$
Blue Graph: $latex y={{x}^{3}}-4{{x}^{2}}+3x$

Extremes without Calculus

There was an interesting question last week on the AP Calculus Community Bulletin Board. A teacher was working with polynomial functions in her pre-calculus class and the class had learned how to find the roots, and how the roots and their multiplicities affected the graph. Her question was whether there is a way to determine…

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October

School is underway and I hope things have settled down for you. You may need a little break so I suggest you give the Calculus Humor website a look. You‘ll find some humorous things there such as the graph at the top of this post. As the name suggests they are all based on calculus.…

Power Rule Implies Chain Rule

Having developed the Product Rule  and the Power Rule  for derivatives in your class, you can explore similar rules for the product of more than two functions and suddenly the Chain Rule will appear. For three functions use the associative property of multiplication with the rule above: So expanding with a slight change in notation: For…