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Explain how the instantaneous rate of change could be used to locate the local maximum and local minimum for a polynomial function

User Vadyus
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For a polynomial function the instantaneous rate of change could be used to locate local maximum and local minimum because when the instantaneous rate of change is 0 there is a local maximum or minimum.

Or in other words when the instantaneous rate of change goes from negative to positive, there are a local minimum of the function. (when the rate of change is 0)

And when the instantaneous rate of change goes from positive to negative, there are a local maximum of the function.

Remember that the instantaneous rate of change represents the slope of the tangent line to the cuve at that point. Slope zero represents a horizontal tangent line and that only happens when there is a local minimum or maximum.

User Bhavana Vadodariya
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