Uploaded October 2024 | Updated September 2026, 1 week ago
How can we find the minimum value of f(x,y)=(x+2/y)(y+8/x) for x and y both positive? This sounds like a multivariable calculus problem, but we don't need to use the Lagrange multiplier method. In fact, an easier way is to use the AM-GM inequality.
0:00 We can use algebra
4:53 Proof of the AM-GM inequality
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Ben D, Grant S, Mark M, Phillippe S. Michael Z, Jan P. Devun C. Stefan C. Ethan BW Didion S. NN Minkyu Y Brandon F Levon M shortsleeve Jack P Gabriel G David H Mateo F Emma M
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#blackpenredpen #math #calculus #apcalculus
How can we find the minimum value of f(x,y)=(x+2/y)(y+8/x) for x and y both positive? This sounds like a multivariable calculus problem, but we don't need to use the Lagrange multiplier method. In fact, an easier way is to use the AM-GM inequality.
0:00 We can use algebra
4:53 Proof of the AM-GM inequality
----------------------------------------
Big thanks to my Patrons for the full-marathon support!
Ben D, Grant S, Mark M, Phillippe S. Michael Z, Jan P. Devun C. Stefan C. Ethan BW Didion S. NN Minkyu Y Brandon F Levon M shortsleeve Jack P Gabriel G David H Mateo F Emma M
💪 Support this channel and get my math notes by becoming a patron: patreon.com/blackpenredpen
🛍 Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
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#blackpenredpen #math #calculus #apcalculus
