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

3-175.

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).