Section 3.1:Tangents and the Derivativeat a PointMath 21A, Spring 2020, UC Davis
What Now, What Next?2.1Rates of Change and Tangents to Curves2.2Limit of a Function and Limit Laws2.3The Precise Definition of a Limit· · ·3.1Tangents and Derivatives at a Point3.2The Derivative as a Function3.3Differentiation Rules· · ·
Slope and Tangent LineDefinitionTheslope of the curve=( )at the point(x0,f(x0)) is the numberm= limh→0f(x0+h)-f(x0)h,provided the limit exists. Thetangent lineto thecurve at (x0,f(x0)) is the line through (x0,f(x0))with this slope.
Slope and Tangent LinePicture
ExampleFind the slope of the curvey=x2at the point(1,1).
Derivative at a PointDefinitionThederivative of a function