CPM Homework Help : CALC Problem 3-76

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

3-76.

Compare three different methods to find a derivative of f(x) =2x³ − x. 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)?

Step 1(a):

Step 2(a):

Expand the numerator.

Step 3(a):

Combine like terms to simplify the numerator.

Step 4(a):

Factor out an h.

Step 5

Simplify the fraction by 'cancelling out' the h.

Step 6

Evaluate the limit as h→0.

Hint (b):

If your answers do not agree, you probably made an Algebraic error in part (a).

Steps (c):

also sketch the f '(x) you found in part (a) and part (b).

Answer (c):

The two graphs should be close, but not identical since part (c) uses a finite value for h.

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