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Aus Online Mathematik Brückenkurs 2

The derivative f−4  gives the function's instantaneous rate of change at the point x=−4, i.e. it is a measure of the function's value changes in the vicinity of x=−4.

In the graph of the function, this derivative is equal to the slope of the tangent to the curve of function at the point x=−4.

y=kx+m where k=f−4 

Because the tangent is sloping upwards, it has a positive gradient and therefore f−40 .

At the point x=1, the tangent slopes downwards and this means that f10 .

y=kx+m where k=f1