Implicit Differentiation

I’ve never liked memorizing formulas. I would rather know where they came from or be able to tie it to something I already know. One of my least favorite formulas to remember and explain was the formula for the second derivative of a curve given in parametric form. No longer. If  and, then the tradition…

Foreshadowing the Chain Rule

I assigned another very easy but good problem this week. It was simple enough, but it gave a hint of things to come. Use the Product Rule to find the derivative of . Since we have not yet discussed the Chain Rule, the Product Rule was the only way to go.  And likewise for higher…

Lin McMullin’s Theorem

Mathematics more often tends to delight when it exhibits an unanticipated result rather than conforming to … expectations. In addition, the pleasure derived from mathematics is related in many cases to the surprise felt upon the perception of totally unexpected relationships and unities. – Mario Livio,  The Golden Ratio I have a theorem named after…