Use Lagrange multipliers to find the extreme values of the function subject to the given constaint. f(x, y, z) = xy2z;  x2 + y2 + z2 = 36

Q: Find the derivative of the following function using the Fundamental Theorem of Calculus. F'(x) =…

A: To find the derivative of the following function by using the Fundamental Theorem of Calculus.

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Q: Let f(x, y) = y³-24x -3x²y. Find all local extreme points of f(x, y) and classify them.

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Q: Evaluate the definite integral. Use a graphing utility to verify your result. 66²x³ x³(2x4 + 3)² dx

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Q: If f(x) = 5x² +7x+7 √x then:

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Q: If f(y) = cos-¹(3y¹), find f'(y). Use exact values. f'(y) = =

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Q: 55. {Use of Tech} Spring oscillations A spring hangs from the ceiling at equilibrium with a mass…

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Q: 6. Consider the three points in the plane and their masses: P₁(5,-1) with m₁ = 4, P₂(-1,4) with m2 =…

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Q: Let f(x) = pit -1-7x Then f'(x) = Write the equation of the tangent line to f(x) at x = 0:

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Q: 15. Consider the graphs of the functions shown below. Which functions have inverses? V N I. III. (a)…

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Q: Use linear approximation, i.e. the tangent line, to approximate √64.4 as follows: Let f(z) = √. The…

A: By using linear approximation, i.e. the tangent line, to approximate .