### Home > CALC > Chapter 3 > Lesson 3.2.3 > Problem 3-76

3-76.

Compare three different methods to find a derivative of

*f*(*x*) =2*x*^{3}−*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*.