Acute angles between the curves (vectors) (KristaKingMath)

Learn how to find the acute angles between two curves by finding their points of intersection, and then the equations of the tangent lines to both curves and the points of intersection. Once you have equations for the tangent lines, you can use the corollary formula for cos(theta) to find the acute angle between the two lines.

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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?!”

[edris]

Boy you really "dumbed" this down for us. Appreciate it. There is nothing my book about this and my professor didn't bother teaching us. 

[hg.]

To the Best math teacher on YouTube, a picture of intersecting curves and their tangents would be helpful, that would give heads up about "derivative coming" too.
Since Krista is the best math teacher on YouTube, a 2nd play is all that's needed to clear things up.

[Tahkoyakii]

Hi! At 13:40, why can you move it into the x + y form to turn it into vector form? I don't understand ? Are we trying to mimic the i j k form?

[lukassanting]

What do you do if you have an equation where you can't isolate y or x on both equations, e.g... m: x^2 - 20x + 100 -3y = 0 and n: y^2 - 20y + 100 - 3x = 0

[MrChipmunk]

Thank you so much. This was incredibly helpful!

[kumaranselvaraju]

Mam Can you represent the result of this video in pictorial form?

[hg.]

This is "long" by Krista's standards. Maybe the learning objective on this one would have been better served with a simpler set of curves that only had one point of intersection.