Find the absolute maximum and minimum values of f(x,y) = 2x^3 + y^4 + 8 on the set D, where D =...
Question:
Find the absolute maximum and minimum values of {eq}f(x,y) = 2x^3 + y^4 + 8 {/eq} on the set {eq}D {/eq}, where {eq}D = \left \{ (x,y)\mid x^2 + y^2 \leq 1 \right \} {/eq}.
Extrema on a Closed Region:
To find the global extreme values, we need to first look for any critical points that lie in the region. Then we need to check the function values on the boundary curve {eq}x^2+y^2=1. {/eq}
Answer and Explanation: 1
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View this answerFind the first partial derivatives.
{eq}f_x(x,y) = 6x^2 \\ f_y(x,y) = 4y^3 {/eq}
There is only one critical point and it occurs at ...
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Using Differentiation to Find Maximum and Minimum Values
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Chapter 9 / Lesson 4
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The extreme values on a graph, the minimum and the maximum values, are called extrema. Learn more about extrema, as well as finding extrema using differentiation.
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