Find the absolute maximum and minimum values of f on the set D. f(x,y) = x^{4} + y^{4} - 4xy + 6,...


Find the absolute maximum and minimum values of {eq}f {/eq} on the set {eq}D {/eq}.

{eq}f(x,y) = x^{4} + y^{4} - 4xy + 6, \quad\quad D = \{(x,y) \left| \right. 0 \leq x \leq 3,\;\; 0 \leq y \leq 2\} {/eq}

Comparison of function using Calculus:

If we want to compare {eq}f(x) \ \ \text{and} \ \ g(x) {/eq} consider a function {eq}\phi(x) = f(x) - g(x) {/eq} or {eq}\phi(x) = g(x) - f(x) {/eq} and check whether {eq}\phi(x) {/eq} is increasing or decreasing in given domain of {eq}f(x) \ \ \text{and} \ \ g(x) . {/eq}

Answer and Explanation: 1

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{eq}\hspace{30mm} \displaystyle{ f(x,y) = x^4 + y^4 - 4xy + 6 \\ f_{x} = 4x^3 - 4y \\ f_{y} = 4y^3 - 4x } {/eq}

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Finding Minima & Maxima: Problems & Explanation


Chapter 5 / Lesson 2

One of the most important practical uses of higher mathematics is finding minima and maxima. This lesson will describe different ways to determine the maxima and minima of a function and give some real world examples.

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