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Problem 110

Find the equation of the tangent plane to the graph of $$ z=f(x, y)=x^{2}+2 y^{2}-1 $$ at the points (a) \(\left(\mathrm{x}_{0}, \mathrm{y}_{0}\right)=(0,0)\) (b) \(\left(\mathrm{x}_{0}, \mathrm{y}_{0}\right)=(1,1)\).

Expert verified

The tangent planes to the graph of \(z = x^2 + 2y^2 - 1\) at the given points are:
(a) at (0, 0): \(z = -1\)
(b) at (1, 1): \(z = 2x + 4y\)

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Chapter 4

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Chapter 4

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Chapter 4

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