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Find the maximum and minimum values of the function f ( x , y ) = x 2 y f(x,y)=x2y subject to 3...

Question:

Find the maximum and minimum values of the function f ( x , y ) = x 2 y f(x,y)=x2y subject to {eq}3 x 2 + 5 y 2 = 45 3x^2+5y^2=45 {/eq}

Maximum and Minimum

We can find the Absolute extremes of a function of two variables with the Lagrange multipliers, first, we find the critical points of the function, then we compare the points, the highest is the Absolute maximum value.

Answer and Explanation:

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We have the function

{eq}f(x,y)=x^{2}y {/eq}

Differentiating the function

{eq}f_x=2\,xy \\ f_y={x}^{2} \\ {/eq}

Constraints:

{eq}g_{x,y}=...

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Solving Min-Max Problems Using Derivatives

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Chapter 15 / Lesson 1
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Max and min problems show up in our daily lives extremely often. In this lesson, we will look at how to use derivatives to find maxima and minima of functions, and in the process solve problems involving maxima and minima.


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