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1 year ago in Number Systems By Manpreet Jaiswal

How can zero-derivative points be determined without using derivatives?

I'm exploring foundational concepts in analysis and pre-calculus pedagogy. I need methods that reveal where a function's rate of change is zero, using reasoning from inequalities, geometry, or function properties, to build intuition before introducing formal differentiation.

RealNumbers Limit DerivativePoints

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By Meghna R Answered 1 year ago

Absolutely. In my work, especially when building intuition before formal calculus, I rely heavily on analyzing a function's inherent properties. Look for symmetry; for instance, a quadratic's vertex is on its axis of symmetry, which you can find algebraically. For polynomials, factoring can reveal repeated roots where the graph "touches" the axis. Graphically, you can often bound a maximum or minimum by constructing inequalities or examining the function's behavior at boundaries and key values. These methods reinforce a deeper, more intuitive understanding of change.

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How can zero-derivative points be determined without using derivatives?

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