If f'(x)=abs(x-2) draw a possible graph

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To find the antiderivative of f'(x) = |x - 2|, the function can be split based on the value of x. For x ≥ 2, |x - 2| simplifies to x - 2, while for x < 2, it becomes -(x - 2). The antiderivative can be computed separately for these intervals, leading to a piecewise function. The graph of the original function will reflect these changes, showing a linear increase with a vertex at x = 2. Understanding how to handle absolute values is crucial for accurately sketching the graph.
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Homework Statement



If f'(x)=abs(x-2) draw a possible grpah of the original function.


The Attempt at a Solution



I can't remember how to find the antiderivative of an absolute value.
Cant some one please enlight me?
 
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martin123 said:

Homework Statement



If f'(x)=abs(x-2) draw a possible grpah of the original function.


The Attempt at a Solution



I can't remember how to find the antiderivative of an absolute value.
Cant some one please enlight me?

|x - 2| = x -2 if x >= 2
and
|x - 2| = -(x -2) if x < 2
 

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