Theorem: The less you know, the more money you make - PowerPoint PPT Presentation

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Theorem: The less you know, the more money you make

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  1. Theorem: The less you know, the more money you make • Proof:We know thata) Time is Money (T=M)b) Knowledge is Power (K=P)and from Physicsc) Power = Work / Time (P=W/T) • By substitution, K = W/M • Rearrange the equation and M = W/K, or Money = Work/Knowledge • From this equation, it follows that as knowledge goes to 0, money goes to infinity.

  2. slope Consider the function We could make a graph of the slope: Now we connect the dots! The resulting curve is a cosine curve.

  3. slope We can do the same thing for The resulting curve is a sine curve that has been reflected about the x-axis.

  4. Derivative of y=sinx • Use the definition of the derivative To prove the derivative of y=sinx is y’=cosx.

  5. Derivative of y=sinx Shortcut: y’=cosx The proof of the d(cosx) = -sinx is almost identical

  6. Derivative of y=tanx • Use the quotient rule to show the derivative is y’=sec2x The proof of the d(cotx) = -csc2x is almost identical Shortcut: y’=sec2x

  7. Derivative of y=secx • Use the quotient rule to show the derivative is y’=secxtanx The proof of the d(cscx) = -cscxcotx is almost identical Shortcut: y’=secxtanx

  8. Summary of trig derivatives p

  9. Practice Time Now for a worksheet