Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.1 Surfaces and Level Curves, #30 · Multivariable Calculus · Partial derivatives

Prove that if … and … then their average …, … has…

Prove that if $x_{1} y_{1} = 1$ and $x_{2} y_{2} = 1$ then their average $x = \frac{1}{2} (x_{1} + x_{2})$ , $y = \frac{1}{2} (y_{1} + y_{2})$ has $x y \geq 1$ . The function $f = x y$ has convex level curves (hyperbolas).

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.1 Surfaces and Level Curves, #30

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