We’ll consider two nagging questions from Calculus I:
1) Students, beginning and advanced, are often confused by the difference between power functions, such as and exponential functions, such as g(x) = . If the derivative of is 3 , shouldn’t the derivative of be ? How did it get to be And what about differentiating Should the answer be Calculus texts often stress that that power functions and exponential functions are different species and have to be treated differently. In this talk, we’ll present a Unified Theory of Functions that shows we can differentiate both types of functions using exactly the same method!
2) Is there a “natural” way to discover the antiderivative of the secant function?
Everything in this talk will be completely understandable to anyone who has completed Calculus I or is currently taking the course.
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