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Unformatted text preview: 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 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....
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This note was uploaded on 04/01/2012 for the course MATH 131 taught by Professor Allen during the Fall '08 term at Texas A&M.
- Fall '08