Given x³ + xy - 4x = 4: dy (a) Find by differentiating implicitly. Do not substitute for y. dx dy dx dy dx (b) Solve the equation for y as a function of x, and find from that equation. y dy dx (c) Confirm that the two results are consistent by expressing the derivative in part (a) as a function of x alone. dy dx = ||

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A: We can use Lagrangian multipliers: Here, the function to be optimized is fx, y, z=x+y2+12z+12. The…

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A: We can solve this as follows:

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A: Let's find maximum and minimum rate of change.

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A: I am attaching image so that you understand each and every step.

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A: This question can be solved using the concept of limits.

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A: Explained below

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A: lim          (6t2 + t -5)/(9-2t2 ) t -->-∞ here question is of limit  and here we have to divide…

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A: Explained below

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A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

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A: We can answer first question as per the honor policy. Please resubmit other question as well to know…

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Q: 6x² - 2x - 1 4x³ X jo dx

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