Sec 3.7 Implicit ‘Functions’ and
Differentiation
We are used to seeing ‘explicit’
functions.
These can be written as 
.
In an implicit ‘function’
the variables are NOT separated on either side of the equation by the equal
sign, and it might be difficult or impossible to do so.
Ex. a) 
b) 
Even just plotting points can be
difficult with implicit ‘functions’.
a) let 
, and find the associated y-value.
What is the slope of the line tangent
to this graph at ?
Differentiate implicitly.
We will assume that y is a function
of x.
Apply the differentiation operator 
(derivative with
respect to x) to both sides of the
equation.
Ex 1) 
Ex 2) 
Ex 3) 
Ex 4) 
Ex 5)
Ex 6) Find
the equation of the line tangent to the graph of
at
the point 
.