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Lösung 1.1:1a

Aus Online Mathematik Brückenkurs 2

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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.
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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.
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[[Image:1_1_1_a1.gif|center]]
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Because the tangent is sloping upwards, it has a positive gradient and therefore f'(-4)>0.
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At the point x=1, the tangent slopes downwards and this means that f'(1)<0.
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Version vom 15:24, 5. Sep. 2008

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.


Image:1_1_1a-1(2).gif
Image:2_1_1a-2(2).gif
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_1.1:1a“