anonymous
  • anonymous
calculus: how do i know if it's relative minima or relative maxima?
Mathematics
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anonymous
  • anonymous
calculus: how do i know if it's relative minima or relative maxima?
Mathematics
jamiebookeater
  • jamiebookeater
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
http://www.themathpage.com/acalc/max.htm hope this helps
anonymous
  • anonymous
thank you! :D
Empty
  • Empty
You probably know a relative min or max happen at slope of zero, since that's when the curve is flat. But how do you distinguish them? Let's just look at a simple case: |dw:1440518537984:dw| Imagine yourself walking along the parabola \(y=x^2\). On your way to the minima, your slope is negative, since you're moving down, but when you're at the minima, of course your slope is zero. Then you keep following the curve and notice your slope has become positive now. So what's changing here? The slope was negative then zero then positive, so really the slope is what is continually increasing, this is what tells us we went through a minima. So the second derivative has to be positive at the minima for us to know that it is a minima.

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