This final unit in the study of calculus AB begins with a discussion of inverse functions and the algebraic and geometric relationship between a function f and its inverse f -1 . The geometric property of f -1 as a reflection of f across the line y = x is used to develop a formula for finding the derivative of f -1 from f .
Next is an introduction to the function f (x) = e x and its inverse f (x) = ln(x) . After a brief discussion of the properties of these functions, we see that the derivative of f (x) = e x is in fact e x itself, and that the derivative of f (x) = ln(x) is the function , which is the only power function that could not be integrated by reversing the power rule. The derivatives of e x and ln(x) are used to develop methods to differentiate functions where x is in the exponent. Finally, the general form of functions that exhibit exponential growth or decay is presented.
Take a Study Break!