Average Rate of Change Over an Interval
Key Questions
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Answer:
Yes.
Explanation:
Remember that the rate of change could be things like acceleration, not just speed.
Even though speed itself is a scalar and cannot be negative, you can have a negative velocity by adding direction (which makes it a vector)
Also, if your speed is decreasing, you decelerate, which is another word for negative acceleration.
For example, let's say you had the function
#sin(x)# to show the speed in respect to time.graph{sinx [-10, 10, -5, 5]}
We can see that your speed increases until it reaches a certain point. There, we see that it decreases to a certain point. The decrease represents negative rate of change. (Deceleration in this case.)
Questions
Derivatives
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Tangent Line to a Curve
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Normal Line to a Tangent
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Slope of a Curve at a Point
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Average Velocity
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Instantaneous Velocity
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Limit Definition of Derivative
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First Principles Example 1: x²
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First Principles Example 2: x³
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First Principles Example 3: square root of x
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Standard Notation and Terminology
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Differentiable vs. Non-differentiable Functions
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Rate of Change of a Function
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Average Rate of Change Over an Interval
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Instantaneous Rate of Change at a Point