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QuestionArt
Find the point(s) on the surface at which the tangent plane is horizontal.
z= 9−x 2 −y 2 + 8y
(x,y,z)=(…)
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Answer
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Step 1I'll solve this step by step, carefully following the LaTeX formatting guidelines:
Step 2: Find the partial derivatives
\frac{\partial z}{\partial y} = -2y + 8
To find points where the tangent plane is horizontal, we need to find where the partial derivatives with respect to x and y are both zero. Partial derivative with respect to x: Partial derivative with respect to y:
Final Answer
The point where the tangent plane is horizontal is (0, 4, 25).
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