1A_1_Slope_of_a_nonlinear_curve - f ( X ) evaluated at that...

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Slope of a nonlinear curve Finding the slope of a straight line of the form Y = a + bX is rather simple: the slope is given by b . What about the more general case of the unspecified equation Y = f ( X )—How do we find its slope? If f ( X ) is nonlinear, its slope may be different at each point, but as long as the function is continuous and differentiable at a particular point, its slope is given by the derivative of
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Unformatted text preview: f ( X ) evaluated at that point. Consider for example the nonlinear continuous and differentiable function Y = f ( X ) = X 2 + 4. Suppose we want to know its slope at the point (X, Y) = (3, 13). The derivative of this function is f ( X ) = 2 X , which takes on the value 6 when X = 3. Hence, the slope of this function is 6 at the point (3, 13)....
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This note was uploaded on 05/03/2010 for the course BUSINESS econ203 taught by Professor Shivaggo during the Spring '10 term at Columbia College.

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