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martin123
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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?
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?
F'(x) = abs(x-2) represents the derivative of the function f(x) at any given point x. The absolute value of x-2 indicates that the slope of the function changes at x=2.
To graph f'(x) = abs(x-2), first plot a point at (2,0) since the derivative is 0 at x=2. Then, on either side of x=2, draw a straight line with a positive slope since the derivative is positive. Finally, connect these lines smoothly at x=2 to create a "V" shaped graph.
The "V" shape of the graph represents a point of inflection where the slope of the function changes from negative to positive or vice versa. In this case, the point of inflection is at x=2 where the derivative changes from negative to positive.
The hole at x=2 is due to the discontinuity of the derivative at that point. Since the absolute value function is not differentiable at x=2, the derivative has a hole at that point.
The graph of f'(x) = abs(x-2) represents the slope of the graph of f(x). Where the graph of f(x) has a positive slope, the graph of f'(x) will be above the x-axis. Where the graph of f(x) has a negative slope, the graph of f'(x) will be below the x-axis. Additionally, the point of inflection on the graph of f'(x) corresponds to a point of maximum or minimum on the graph of f(x).