### Home > CALC > Chapter Ch3 > Lesson 3.4.3 > Problem 3-175

3-175.

Use the *definition of a derivative *as a limit to find the slope function, *f *′(*x*), of *f*(*x*) = 2*x*^{2} − 3*x* + 4. Confirm your slope function with the Power Rule. Then use your slope function to find *f *′(*3*) and *f *′(−2). Homework Help ✎

Hana's definition of the derivative:

1. Substitute *f*(*x*) into Hana's definition

2. Expand the numerator

3. Combine like terms

4. Factor out an *h*

5. Cancel out the *h*

6. Evaluate the limit as *h*→0

This is *f* '(*x*)

Use the Power Rule to find *f* '(*x*). Compare to the *f* '(*x*) you found algebraically. If they do not agree, you probably made an algebraic error.

Evaluate *f* '(3) and *f* '(−3).