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13112an2b.1-3 - c Kendra Kilmer Section 2.6 Derivatives and...

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c circlecopyrt Kendra Kilmer January 23, 2012 Section 2.6 - Derivatives and Rates of Change Recall : The average rate of change can be viewed as the slope of the secant line between two points on a curve. In Section 2.1, we numerically estimated the slope of a tangent line (instantaneous rate of change) by calculating the slopes of secant lines nearer and nearer to the point of tangency and determined what value they approached. In actuality, we were numerically taking the limit of the slopes of the secant lines. Definition: The derivative of a function f at a number a , denoted by f ( a ) , is provided that this limit exists. Interpretations of the Derivative The derivative has various applications and interpretations, including the following: 1. Slope of the tangent line: f ( a ) is the slope of the line tangent to the graph of f at the point ( a , f ( a )) . 2. Instantaneous rate of change: f ( a ) is the instantaneous rate of change of y = f ( x ) at x = a .
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