Rolle's Theorem - Lesson+Exploration+Practice
Explore the function and find the points at which the [i][color=#ff0000]Rolle's Theorem[/color][/i] for a real function holds true.[br][br]Define the [color=#0000ff][i][color=#ff0000]function[/color] [/i][color=#000000]in the[/color][/color] [color=#ff0000][i]f[/i]([i]x[/i])[/color] box, and the [i]start point [b]a[/b] [/i]and[i] end point[/i] [b][i]b[/i][/b] of the interval in the related boxes (you can also drag points [b][i]a[/i][/b] and [b][i]b[/i][/b] in the [i]Graphics View[/i]).[br]Move point [b][color=#38761D][i]c[/i][/color][/b] along the [i]x[/i]-axis to view the tangent line to the function graph, as well as the value of its slope in the left View.
For each problem, determine if [i]Rolle's Theorem[/i] can be applied. [br]If it can, find all values of [i]c[/i] that satisfy the theorem. If it cannot, explain why.[br][br][math]f(x)= 1 + |x|[/math] in [math][-1,1][/math][br][math]f(x)= -x^2-x+2[/math] in [math][-1,0][/math][br][math]f(x)=\sqrt(1-x^2)[/math] in [math] [-1,1][/math]