Lösung 1.1:1a

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.

Because the tangent is sloping upwards, it has a positive gradient and therefore f'(-4)>0.

At the point x=1, the tangent slopes downwards and this means that f'(1)<0.