Use the definition of a derivative as a limit to find f ′(x) if f(x) = 2x + 9. Use the Power Rule to confirm your solution. Homework Help ✎
Hana's definition of the derivative:
Substitute f(x) into Hana's definition of the derivative.
Expand the numerator and combine like terms.
Factor out an h from the numerator so you can 'cancel out' the h from the denominator.
Evaluate the limit as h →0. This will give you f '(x).
Confirm that the f '(x) you found Algebraically agrees with what you get using the Power Rule.