The derivative of a function is interpreted as the slope of the tangent line to the curve of the function at a certain given point. In this section, we will explore the meaning of a derivative of a function, as well as learning how to find the slope-point form of the equation of a tangent line, as well as normal lines, to a curve at multiple given points.
• Point-Slope Form of a line with slope m through a point (x1,y1):m=x−x1y−y1
• Tangent Line & Normal Line
The normal line to a curve at a particular point is the line through that point and perpendicular to the tangent line.
Connecting: Derivative & Slope & Equation of Tangent Line Exercise: The graph of the quadratic function f(x)=21x2+2x−1 is shown below.
Determining Equations of the Tangent Line and Normal Line
Consider the function: f(x)=32x(x+3x)
Locating Horizontal Tangent Lines
Determining Lines Passing Through a Point and Tangent to a Function
Consider the quadratic function: f(x)=x2−x−2
Locating Lines Simultaneously Tangent to 2 Curves
Consider the quadratic functions: f(x)=x2 g(x)=41x2+3
Slope and equation of tangent line
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