Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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**Exercise Set**

11. Find an equation of the tangent plane to the surface \( \sqrt{x} + \sqrt{y} + \sqrt{z} = 4 \) at the point \( P(4, 1, 1) \).

12. Find the local maximum and minimum values and saddle point(s) of the function \( f(x, y) = -x^4 + 4xy - 2y^2 + 1 \).

13. Find the maximum value of the function \( f(x, y) = 6 - 4x^2 - y^2 \) subject to the constraint \( 4x + y = 5 \).

14. Find the maximum and minimum values of the function \( f(x, y) = xy \) on the ellipse given by the equation \( x^2 + \frac{y^2}{4} = 1 \).
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Transcribed Image Text:**Exercise Set** 11. Find an equation of the tangent plane to the surface \( \sqrt{x} + \sqrt{y} + \sqrt{z} = 4 \) at the point \( P(4, 1, 1) \). 12. Find the local maximum and minimum values and saddle point(s) of the function \( f(x, y) = -x^4 + 4xy - 2y^2 + 1 \). 13. Find the maximum value of the function \( f(x, y) = 6 - 4x^2 - y^2 \) subject to the constraint \( 4x + y = 5 \). 14. Find the maximum and minimum values of the function \( f(x, y) = xy \) on the ellipse given by the equation \( x^2 + \frac{y^2}{4} = 1 \).
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