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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| + | [[Image:1_1_1_a2.gif|center]] | ||
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<center> [[Image:1_1_1a-1(2).gif]] </center> | <center> [[Image:1_1_1a-1(2).gif]] </center> | ||
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<center> [[Image:2_1_1a-2(2).gif]] </center> | <center> [[Image:2_1_1a-2(2).gif]] </center> | ||
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| - | [[Image:1_1_1_a1.gif|center]] | ||
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| - | [[Image:1_1_1_a2.gif|center]] | ||
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.
