Graphing The Derivative of a Function
Remember: The derivative of a function f(x) at x = a, if it even exists at x = a, can be geometrically interpreted as the slope of the tangent line drawn to the graph of f at the point (a, f(a)). Hence, the y-coordinate (output) of the pink point = the slope of the tangent line drawn to the graph of f(x) at the BIG BLACK POINT. (Note that the pink point and the BLACK POINT always have the same x-coordinate.) By calculating the slope at several values, we can trace the graphs of f'(x).