| 11. | To every point on this surface, there is an infinite number of tangent lines.
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| 12. | Take a small step along that tangent line up to a point A _ 1.
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| 13. | Geometrically, the derivative is the slope of the tangent line to the graph of at.
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| 14. | The tangent line is the best linear approximation of the function near that input value.
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| 15. | For example, a curve that crosses itself doesn't have a unique tangent line at that point.
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| 16. | So, the other intersection point between the tangent line and the graph of is the point
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| 17. | The angle between two curves intersecting at a point is the angle between their tangent lines.
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| 18. | This hypotenuse is parallel to the tangent line of the integral curve at that corresponds to.
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| 19. | The slope M should be, most accurately, the slope of the tangent line at x = a.
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| 20. | In this case, we use the tangent line to the curve at this point as our line.
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