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  1. Compare three different methods to find a derivative of f(x) =2x3x. Homework Help ✎

    1. Use the definition of a derivative.

    2. Use the Power Rule. Do your answers agree?

    3. 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.