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Home Differentiation Derivatives Examples Example 4: Absolute Value Function  
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Example 4: Absolute Value Function
Case 1 Find the derivative of f(x) = x. x > 0. In this case x = x, and we have Case 2 x < 0. Now x =  x, and Case 3 x = 0. Then and The standard part of Δy/Δx is then 1 for some values of Δx and 1 for others. Therefore f'(x) does not exist when x = 0. In summary,
Figure 2.1.6 shows f(x) and f'(x). Figure 2.1.6 The derivative has a variety of applications to the physical, life, and social sciences. It may come up in one of the following contexts.


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