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13112an2b.4-7

# 13112an2b.4-7 - c Kendra Kilmer Section 2.7 The Derivative...

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c circlecopyrt Kendra Kilmer January 23, 2012 Section 2.7 - The Derivative as a Function Recall: The derivative of a function f at a specific number a is given by If the number a is allowed to vary, we obtain a new function called the derivative of f , f ( x ) , which is defined as Other Notations for the Derivative of y = f ( x ) : f ( x )= y = dy dx = d f dx = d dx f ( x ) Example 1: Given the graph of f ( x ) below, estimate the value of f ( x ) at the following points: -1 -2 -3 -4 -5 -6 5 4 3 2 1 -7 -8 7 8 6 x y 9 1 6 5 4 3 2 -5 -4 -3 -2 -1 f(x) x 6 3 1 1 4 f ( x ) Conclusion: 4

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c circlecopyrt Kendra Kilmer January 23, 2012 Example 2: Find f ( x ) if f ( x )= 1 x 2 + x . State the domain of f ( x ) and f ( x ) . Nonexistence of the Derivative If f ( a ) does not exist, then we say that f ( x ) is nondifferentiable at x = a . This occurs when the graph: 1. 2. 3. 5
c circlecopyrt Kendra Kilmer January 23, 2012 Example 3: For what values of x is f nondifferentiable?

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13112an2b.4-7 - c Kendra Kilmer Section 2.7 The Derivative...

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