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12345Derivative functions


Any function y = f ( x ) usually has a slope at any point of its curve that is given by the derivative f ' ( x ) of that point.

You can now also make a graph of the values of these slopes (derivatives). Here you see the curve of a function (in red) together with the corresponding graph (in blue), the graph given by f ' .
The function f ' is called the slope function or derivative function.

If you compare the two curves you can see that:

  • the values of the slope function are positive while the original function is increasing;

  • the values of the slope function are negative while the original function is decreasing;

  • at values of x where the slope function has a value of 0 , the original function has a horizontal tangent; these are often extrema of the original function. .

It is therefore primarily the sign (positive, negative or 0 ) of the derivative function that provides information about the curve of the original function.

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