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2.7 Tangents, Velocities, & Rates of Change

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Curve C has equation y = f(x). To calculate the slope of a secant segment from point P to point Q, we use

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But what if we want the EXACT slope of the tangent line at point P??? DEFINITION: The tangent line to the curve y = f(x) at the point P (a, f(a)) Is the line through P with slope Example: Find an equation of the tangent line to the parabola at the point P (1,1)

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We can also use the following (similar) equation for slope: Find an equation of the tangent line to the hyperbola at the point (3,1)

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Velocity: Average velocity Instantaneous velocity

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Read 2.7 p Work p. 155 #1, 3, 6, 11, 15, 17, 24

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