Slope stability is a measure of the magnitude in which the slope of the function changes over any given interval. Slope stability is easily quantified using introductory calculus in the first derivative test for critical points. The test for slope stability is often used in processes that involve optimization of equations in the mapping of related rates using differentials. A change in slope is also useful for mapping a function when the equation itself is unknown and only specific data points are available.
Instructions
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1
Take the first derivative of a function over the desired interval.
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2
Set the resultant derivative equation equal to zero and solve for all values of "X."
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3
Subtract the endpoint of the interval from the beginning point of the interval and take its absolute value.
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4
Divide the number of times an "X" value, solved in Step 2, appears in the desired interval by the absolute value of the interval itself. The resultant ratio is the stability of the slope in terms of how often the slope changes over the given range of values.