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opus

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## Homework Statement

Use the graph (attached below) to determine the time intervals when the velocity is positive, negative, or zero.

## Homework Equations

## The Attempt at a Solution

The graph is of a position function.

Velocity is the derivative of position.

Velocity will be zero when the derivative of the position function is zero. In other words, where the tangent line to a point on the graph of the position function is horizontal.

On the intervals (2,5) it is clearly horizontal. However, at x=1.5 and x=6, the velocity should also be zero because the derivative at these points would be a horizontal tangent line.

Now in my book, it says that the velocity is zero on (2,5). And that is all.

Is my reasoning off with this? The velocity should be zero on the interval (2,5) as well as at the points x=1.5 and x=6.