Applet: Derivative of interpolating polynomial
The blue curve is the graph of a polynomial $f(x)$. You can change $f$ by dragging the blue points, as $f$ is an interpolating polynomial through those points. The derivative $f'(x)$ of the function $f(x)$ is shown by the green curve. The derivative $f'(x)$ indicates the slope of the function $f(x)$, so that it is positive when $f$ is increasing, negative when $f$ is decreasing, and zero at the points where the tangent line to $f$ is horizontal. To test your ability to estimate the derivative from the function, you can uncheck the “show derivative” checkbox and attempt to sketch what you think the derivative is. Alternatively, you can uncheck the “show function” checkbox to test your ability to sketch the function from its derivative.
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