points-on-the-cone-closest-to-a-point-kristakingmath

Interactive video lesson plan for: Points on the cone closest to a point (KristaKingMath)

Activity overview:

► My Partial Derivatives course: https://www.kristakingmath.com/partial-derivatives-course

► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course

Learn how to find the points on the surface of a cone which are closest to the given coordinate point in three-dimensional space. If you're looking for the points which are closest together, then you're trying to minimize the distance between the points, which means you need an equation for distance between the points, and this will be the equation you optimize. Write out the distance formula in three variables, and then use the equation of the cone to make a substitution into the distance formula so that the distance formula is only in two variables. Take first-order partial derivatives of the distance formula in order to find a critical point. Then plug the critical point back into the equation of the cone to find the corresponding z-values that give the points on the cone closest to the given coordinate point. Use the second derivative test to verify that the critical point does represent a local minimum of the distance function.

● ● ● GET EXTRA HELP ● ● ●

If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com

● ● ● CONNECT WITH KRISTA ● ● ●

Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com

INSTAGRAM // https://www.instagram.com/kristakingmath/
PINTEREST // https://www.pinterest.com/KristaKingMath/
QUORA // https://www.quora.com/profile/Krista-King

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