Consider the surface S of equation z²-2x² + y²-x= 0 and let P (2, 3, 1) be a point at S. Suppose z is an implicit function of x and y in a neighborhood of point P. Consider the following statements: I. There is no direction for which the directional derivative of z in P is -40. Is this true or false?|

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A: Solution

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A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

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Q: 8. Consider the surface S of equation z2-2x? + y²-x= 0 and let P (2, 3, 1) be a point at S. Suppose…

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