2.1 The Derivative Function

• recall:

• Two interpretations:

1) the _________________________ to the graph

()

yfx

=

at point

(, ())

afa

2) the _________________________ rate of change of

()

yfx

=

at

xa

=

• In calculus, this is called the _____________________________________________________

• In general, the derivative function for any function

()

fx

is given by:

• Notation for the derivative of the function

()

yfx

=

• a function is said to be __________________________ at ‘a’ if

'( )

fa

exists

• a function is differentiable on an interval if it is differentiable at every number in the interval

• at points where

()

yfx

=

is not differentiable, we say that the derivative does not exist; examples where the

derivative does not exist:

• a __________________ to the graph of a function at point ‘P’, is the line that is ___________________ to the

tangent line that passes through point ‘P’.

mlenniofath f

h

slopeof the

tangent

instantaneous

derivative of fad af xa

fxhim fCxth

hfirst

h0principles

fxread fprime of x

yread yprime

ddI read deey by dee

Leibniz notation

differentiable

disdontinuity

normal i