Uploaded May 2026 | Updated September 2026, 2 weeks ago
This question is from the multivariable calculus textbook by James Stewart. This is the last question from the "Problems Plus" section in Chapter 14, which is meant to be harder than the usual exercises. The goal is to find the maximum value of the function f(x,y)=(ax+by+c)^2/(x^2+y^2+1). This question would be extremely difficult if you use the Lagrange multiplier method. Instead, let's try the Cauchy-Schwarz inequality!
Proving that dot product formula with the Law of Cosines: youtu.be/mqrTVQsrH7E
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I help students master the basics of calculus. You can show your support and help me create even better content by becoming a patron on Patreon ๐ patreon.com/blackpenredpen
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Want more practice? Get my calculus practice quizzes on Patreon!
Calculus 1 ๐ patreon.com/collection/1703815
Calculus 2 ๐ patreon.com/collection/1716951
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#calculus #bprpcaluclus #mathtutorials #maths #multivariablecalculus
This question is from the multivariable calculus textbook by James Stewart. This is the last question from the "Problems Plus" section in Chapter 14, which is meant to be harder than the usual exercises. The goal is to find the maximum value of the function f(x,y)=(ax+by+c)^2/(x^2+y^2+1). This question would be extremely difficult if you use the Lagrange multiplier method. Instead, let's try the Cauchy-Schwarz inequality!
Proving that dot product formula with the Law of Cosines: youtu.be/mqrTVQsrH7E
----------------------
I help students master the basics of calculus. You can show your support and help me create even better content by becoming a patron on Patreon ๐ patreon.com/blackpenredpen
----------------------
Want more practice? Get my calculus practice quizzes on Patreon!
Calculus 1 ๐ patreon.com/collection/1703815
Calculus 2 ๐ patreon.com/collection/1716951
----------------------
#calculus #bprpcaluclus #mathtutorials #maths #multivariablecalculus
