[i][b][color=#0000ff]The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of function at that point.[/color][/b][/i]

[b][color=#ff0000][i]1.Construct the polynomial f(x) = x^2/2 + 1,[/i][br][i]2.Create new point A on function f(x),[br]3.Create tangent t on function through point A by input t=Tangent(A,f) in input bar,[/i][br][i]4.Create slope of tangent by input m=Slope[t] in input bar,[br]5.Define point B by input B=(x(A).m) in input bar,[/i][br][i]6.Join point A and B,[/i][br][i]7.Trace on for point B,[/i][br][i][url=http://8.to/]8.To[/url] visualize derivative of slope of tangent,drag the point A.[/i][/color][/b]

[list][*][i][b][color=#0000ff]Students will be able to define the derivative of slope of tangent with example.[/color][/b][/i][/*][/list]

Dynamic Applet-

[list=1][*][b][color=#00ff00]Enter the polynomial f(x) = x^2/2 + 1,[/color][/b][/*][*][b][color=#00ff00]Create a new point A on function f. Hint: Move point A to check if it is really restricted to the[/color][/b][/*][*][b][color=#00ff00]function, [/color][/b][/*][*][b][color=#00ff00]Create tangent t to function f through point A. t=Tangent(A,f), [/color][/b][/*][*][b][color=#00ff00]Using Input Box,[/color][/b][/*][*][b][color=#00ff00]create slope of tangent t using: m = Slope[t],[/color][/b][/*][*][b][color=#00ff00]Define point B: B =(x(A), m) Hint: x(A) gives the x-coordinate of point A,[/color][/b][/*][*][b][color=#00ff00]Connect points A and B using a segment,[/color][/b][/*][*][b][color=#00ff00]Trace On for the point B,[/color][/b][/*][*][b][color=#00ff00]Perform the drag test to visualize the derivative as slope of tangent.[/color][/b][/*][/list]