### Home > CALC > Chapter 4 > Lesson 4.3.2 > Problem 4-111

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*) = −*x*^{2}+ 3*x*+ 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* = −*x*^{2} + 3*x* + 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