Compare three different methods to find a derivative of f(x) =2x3 − x. Homework Help ✎
Use the definition of a derivative.
Use the Power Rule. Do your answers agree?
Use your graphing calculator: graph the equation
for h = 0.01. Does the graph match that of f ′(x) from part (a)?
Expand the numerator.
Combine like terms to simplify the numerator.
Factor out an h.
Simplify the fraction by 'cancelling out' the h.
Evaluate the limit as h→0.
If your answers do not agree, you probably made an Algebraic error in part (a).
also sketch the f '(x) you found in part (a) and part (b).
The two graphs should be close, but not identical since part (c) uses a finite value for h.