Use the definition of a derivative as a limit to find the slope function, f ′(x), of f(x) = 2x2 − 3x + 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).