8notes.pdf - Section 3.1 Tangents and the Derivative at a Point Math 21A Spring 2020 UC Davis What Now What Next 2.1 2.2 2.3 3.1 3.2 3.3 Rates of Change

8notes.pdf - Section 3.1 Tangents and the Derivative at a...

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Section 3.1: Tangents and the Derivative at a Point Math 21A, Spring 2020, UC Davis
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What Now, What Next? 2.1 Rates of Change and Tangents to Curves 2.2 Limit of a Function and Limit Laws 2.3 The Precise Definition of a Limit · · · 3.1 Tangents and Derivatives at a Point 3.2 The Derivative as a Function 3.3 Differentiation Rules · · ·
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Slope and Tangent Line Definition The slope of the curve = ( ) at the point ( x 0 , f ( x 0 )) is the number m = lim h 0 f ( x 0 + h ) - f ( x 0 ) h , provided the limit exists. The tangent line to the curve at ( x 0 , f ( x 0 )) is the line through ( x 0 , f ( x 0 )) with this slope.
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Slope and Tangent Line Picture
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Example Find the slope of the curve y = x 2 at the point (1 , 1).
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Zooming In
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Derivative at a Point Definition The derivative of a function
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