Compare two different methods for determining a derivative in parts (a) and (b).
Use the definition of the derivative as a limit to write the slope function,
, if .
into the Definition of the Derivative (this is Hana's definition):
Find a way to 'cancel out the
in the denominator:
1. Expand the numerator.
2. Combine like terms.
3. Factor out an
4. Cancel out the
Now that there is no longer an
in the denominator, take the limit as .
This is the derivative of
Use the Power Rule to write an equation for
. Do your answers agree?
If your answers are different, then you probably made an algebraic error in part (a). Find it and fix it.
Use your slope function to calculate