Forx 0 = 1, we can findy 0 by simplysubstitutingintof(x).
Thusthe equationof the tangentline is
Notation
Calculus,just like all branchesof mathematics,is rich with notation.Thereare manywaysto denotethe
derivativeof a functiony=f(x) in additionto the mostpopularone,f(x). Theyare:
In addition,whensubstitutingthe pointx 0 into the derivativewe denotethe substitutionby one of the following
notations:
Existenceand Differentiabilityof a Function
If, at the point(x 0 ,f(x 0 )), the limit of the slopeof the secantline doesnot exist,then the derivativeof the
functionf(x) at this pointdoesnot exist either. That is,
if