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!