Sketch the level curves, z = 1 & z = 4 for the function f(x, y) = x^{1 / 3} y^{2 / 3}, x greater...


Sketch the level curves, {eq}z = 1 \& z = 4 {/eq} for the function {eq}f(x,y) = x^{\frac{1}{3}} y^{\frac{2}{3}}, x > 0, y > 0 {/eq}

Level Curves of Two Variables Functions

Level curves of two variables function are the curves in the plane {eq}z=k {/eq} with equations {eq}f(x,y) = k, {/eq} where the constant {eq}k {/eq} is in the range of {eq}f. {/eq}

Answer and Explanation:

Note that we can rewrite {eq}x^{\frac{1}{3}} y^{\frac{2}{3}} {/eq} as {eq}x^{\frac{1}{3}} (y^2)^{\frac{2}{3}} = (x\cdot y^2)^{\frac{2}{3}}. {/eq}...

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Learn more about this topic:

Graphing & Analyzing Rational Functions

from Precalculus: High School

Chapter 13 / Lesson 2

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