Continuous function [math]f\left(x\right)[/math] and its derivative function [math]f'(x)[/math]. [br][br]Grab the slider and move it left or right to change the position of the points.[br][br]Note that [math]f'(x)=0[/math] when the tangent line to curve [math]f[/math] is horizontal.[br][br]Also, [math]f'(x)[/math] is positive when the tangent line to the curve is increasing while [math]f'(x)[/math] is negative when the tangent line to the curve is decreasing.