Derivative of function
Introduction
-The derivative of a function of a single variable at a chosen input value ,when it exists , is the slop of tangent line to the graph the function at that point.
-In below applet, the graph of function drawn in black and a tangent line to that function drawn in red, the slop of tangent line is equal to the derivative of the function at that marked point.
objectives
Dynamic applet of derivative as a slop of tangent.
User guideline
-Move the point A to show how the slop of tangent line changes.the slop of tangent line is traced in black so,the derivative of the red function is black function.
materials:- dynamic ggb applet
Test your understanding
Q.n Move the points A then there becomes changes in the tangent line and slop of tangent, then which of the colored line indicate the derivative of the function?
Перевірте все, що стосується
- A
- B
Construction protocal
to construct this applet follow the following steps:-
1.At first,enter the polynomials f(x)=x^2/2+1 by using input bar.
2. create the point A on the function f by using the point tool bar.
3.create the tangent line to the function f through the point A i.e input t=tangent(A,f) by using input bar.
4.create the slop of tangent m=slop(t) or input m=slop(<line>) by using input bar.
5.create a point B=(x(A),m) by using input bar.
6. join the line segment A and B.
7. then drag the point A to visualize the derivative as a slop of tangent .also you can decorate your applet by using object properties and save your applet in ggb file.