Title: GeoGebra
Course: Demonstrating STACK (v4.3.7)

Consider the function \({\displaystyle f(x) = [value]}\) whose graph is displayed below.

The tangent line through the point \(([value], [value])\) is also a function. Determine its expression.

You can use the GeoGebra applet below to move the secant line into a tangent line by moving the points A and B. There are other ways to solve this problem.

What is the slope of the tangent line at the pont \(([value], [value])\)?
By slope we mean the ratio of the \(y\)- and \(x\)-coordinate changes of the line.
Answer:

At which point does the tangent line cross the \(y\)-axis?
Give only the value of the \(y\)-coordinate.
Answer:

Formulate the expression of the tangent line by using the formula \(g(x) = kx + b\), where \(k\) is the slope and \(b\) is the point where the line crosses the \(y\)-axis.
Answer: Tangent line's function is \(g(x)\) = .

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

This web page requires Java and it does not work in Google Chrome browser (version 13).
Feedback: Reading from the applet we see that the slope of the tangent line is [value]. The tangent line crosses the \(y\)-axis at the point [value]. Hence, its function on \(x\) is \(g(x) = [value]\).