Three Important Lines In Calculus

[nycmathguy]

Can you graph the following three lines on the xy-plane using a different color per line?

What is the difference between a tangent line, secant line and the normal line?

 

[MathLover1]

A secant line is a straight line joining two points on a function.
Secant line = Average Rate of Change = Slope

A tangent line is a straight line that touches a function at only one point. The tangent line represents the instantaneous rate of change of the function at that one point.

Tangent Line = Instantaneous Rate of Change = Derivative

together

 

[nycmathguy]

A secant line is a straight line joining two points on a function.
Secant line = Average Rate of Change = Slope
View attachment 561
A tangent line is a straight line that touches a function at only one point. The tangent line represents the instantaneous rate of change of the function at that one point.

Tangent Line = Instantaneous Rate of Change = Derivative
View attachment 560



together

View attachment 562

Beautifully done and illustrated.