Slope and equation of tangent line - Derivatives

Slope and equation of tangent line

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=yy1xx1(x_1,y_1): m=\frac{y-y_1}{x-x_1}

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.
  • 1.
    Connecting: Derivative & Slope & Equation of Tangent Line
    Exercise: The graph of the quadratic function f(x)=12x2+2x1f\left( x \right) = \frac{1}{2}{x^2} + 2x - 1 is shown below.
    Slope and equation of tangent line
  • 2.
    Determining Equations of the Tangent Line and Normal Line
    Consider the function: f(x)=x32(x+3x)f(x)=\frac{x}{32}(\sqrt{x}+{^3}\sqrt{x})
  • 3.
    Locating Horizontal Tangent Lines
  • 5.
    Determining Lines Passing Through a Point and Tangent to a Function
    Consider the quadratic function: f(x)=x2x2f(x)=x^2-x-2
  • 6.
    Locating Lines Simultaneously Tangent to 2 Curves
    Consider the quadratic functions:
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Slope and equation of tangent line

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