Compare two different methods to find a derivative. Homework Help ✎
Use the definition of the derivative as a limit to find the slope function, f ′(x), of f(x) = −x2 + 3x + 1.
Use the Power Rule to find f ′(x). Do your answers agree?
Use your slope function to find f ′(0) and f ′(1).
Substitute f(x) into the Definition of the Derivative (this is Hana's definition):
Find a way to 'cancel out the h' in the denominator:
1. Expand the numerator.
2. Combine like terms.
3. Factor out an h.
4. Cancel out the h.
Now that there is no longer an h in the denominator, take the limit as h→0.
This is the derivative of y = −x2 + 3x + 1.
If your answers are different, then you probably made an algebraic error in part (a). Find it and fix it.
f '(0) = 3, f '(1) = 1