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 slopepoint form of the equation of a tangent line, as well as normal lines, to a curve at multiple given points.
Lessons
Notes:
• PointSlope Form of a line with slope m through a point $(x_1,y_1): m=\frac{yy_1}{xx_1}$
• 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 $f\left( x \right) = \frac{1}{2}{x^2} + 2x  1$ is shown below.

2.
Determining Equations of the Tangent Line and Normal Line
Consider the function: $f(x)=\frac{x}{32}(\sqrt{x}+{^3}\sqrt{x})$ 
3.
Locating Horizontal Tangent Lines

5.
Determining Lines Passing Through a Point and Tangent to a Function
Consider the quadratic function: $f(x)=x^2x2$ 
6.
Locating Lines Simultaneously Tangent to 2 Curves
Consider the quadratic functions:
$f(x)=x^2$
$g(x)=\frac{1}{4}x^2+3$