Find the critical points of the function. Then use the Second Derivative Test to determine whether they are local minima, local maxima, or saddle points (or state that the test fails.) f(x, y) = In(x) + 5 In(y) – x – 8y (x, y) = ---Select---

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Q: a) Determine the first derivative. f(x)= x³ - 5x² + 3x + 2 b) Determine critical points, and…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: A function f(x) is defined as: 3 f(x) = x³-2x+ x2 At x = a, where −2 < a < 2, the tangent to the…

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Q: Determine where the function f(x) is decreasing given the first derivative is: ƒ¹(x) = x²(x + 1)

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Q: 3. Find the points (x,y) of the function f(x) = -x³ + 12x² - 5 where the tangent is horizontal AND…

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Q: (B) Use the second derivative test to find the maxima and minima for f(2) = 22 - 15x + 1. 3 %3D

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Q: Use the derivative to determine the local minima and maxima. If a minimum and maximum does not exist…

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Q: 1. f(x)= Vx3 + 2x² + 3 2. f(x) = (6x – 7)(2x + 3)

A: To find the second derivatives of the given functions.

Q: The derivative of f(x) = In(5x³ – 12) Is

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Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

A: Second derivative test is not applicable then we apply first derivative test.

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Q: Find the value(s) of "c" that satisfy the conclusion of the Mean Value Theorem for the derivative of…

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Q: the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function…

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Q: Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable.…

A: The objective is to find relative extrema, if any, of the function.

Q: Find an equation of the tangent line to y = f(x) at x = -2. (Using the definition) f(x)=x² + x² + x…

A: we have, Differentiating w.r.t x, we getDifferentiating again w.r.t x, we getFurther,    .     .…

Q: Find the critical points of the function. Then use the Second Derivative Test to classify the nature…

A: Critical points and classification

Q: Find the critical point of the function. Then use the Second Derivative Test to classify the nature…

A: The given function is .We need to find the critical points and their classification.We know that…