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**2.7 Tangents, Velocities, & Rates of Change**

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**Curve C has equation y = f(x)**

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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Section 1.4 The Tangent and Velocity Problems. WHAT IS A TANGENT LINE TO THE GRAPH OF A FUNCTION? A line l is said to be a tangent to a curve at a point.

Section 1.4 The Tangent and Velocity Problems. WHAT IS A TANGENT LINE TO THE GRAPH OF A FUNCTION? A line l is said to be a tangent to a curve at a point.

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