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M241 - Relation between f(x), f'(x), and tangent.

The two intersection points show when f'(x) = f(x). The relationship between f(x) and f'(x), is that the derivative, f'(x), finds the slope of the function, which is used also for the tangent line. This can also show if the function is increasing or decreasing. The tangent line uses the slope the derivative function provides and the number provided by the slider created. Which then creates a line that touches the parabola at that one specific point along the curve, which changes as x0 changes.