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Assuming the function is linear, the direction of the function can be determined by the coefficient's sign:

[y = mx + b]

Where m is the coefficient of x, if m is negative, then the function is increasing. If m is positive, the function is decreasing (this relationship is rather complicated and requires advanced calculus to prove).

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It shows whether, and how steeply, the terrain or function is increasing or decreasing.


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The intervals are determined by when the derivative is positive or negative, because the derivative is the slope and a negative slope means the function is decreasing. The function y=(x/sqrt(x2))+1, however, can be rewritten as y=x/absolutevalue(x) + 1, and as such will be represented as a pair of parallel lines, y=0 for x<0 and y=2 for x>0. As the lines are horizontal, the function is never increasing or decreasing.


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Yes, a critical point can be where the graph changes its shape without changing its increasing or decreasing behavior. This typically occurs at points of inflection, where the concavity of the graph changes, but the function may still be increasing or decreasing. In such cases, the first derivative does not change sign, while the second derivative does, indicating a change in the curvature of the graph rather than a change in the overall trend.


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Related Questions

What are the intervals over which the function is increasing or decreasing?

It depends on the function.


Is a constant function increasing or decreasing function or both or not?

Neither, by definition.


What if the rate of change is a measure of how fast the function is increasing or decreasing what does the slope of a linear?

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