8. Consider the function f(x) = -2x – 3x? + 36x +4 on the closed interval - 5,5]. Identify the inflection point(s) of f(x) and identify intervals with associated concavities. Identify all of the critical points and verify the local/global max/min within the interval. Verify at least one critical point using FDT and at least one critical point using SDT.

Q: 5. Determine the minimum value of f(x) 3x on the interval [-1,1] %3D

A: Let's find.

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Q: :(- 2,2]– R, F(x) = L(-3(² + 1) dt

A: Given data :  F(x)=∫-2x2(t-3)(t2+1)dt

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A: Given f(x, y) = 3x2 + 2xy + y2 + 4x − 8 by second derivative test to identify any critical points…

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Q: Find the critical points and the intervals on which the function is increasing or decreasing. Use…

A: Critical Points of 5x2+6x-4:Critical points are points where the function is defined and its…

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A: 3.1. The given data is: fx=2 x lnx To determine all the critical numbers to f(x).

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A: Given  ƒ(x) = x3

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Q: 5. Ifc is a critical point of F(x), when the is a local maximum or minimum at c? Explain

A: To give the condition of local maximum or minimum at c if c is a critical point of F(x).

Q: (7) Does the extreme value theorem tell us that f (x) = ! has an absolute maximum and absolt minimum…

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Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: Find the critical points and extreme values of f(x) = -x(x^2-1) on the interval [0,1].

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Q: If c is a critical point of f(x), when is there no local maximum or minimum at c? Explain.

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Q: 6. Determine f such that f"(x) = 12x – 1 and 1 is both a critical number and a y- intercept of f.

A: A differential equation is an equation in x,y and derivatives of y. A linear differential equation…

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Q: Use the Second Derivative Test to classify each critical point of f(x) = x^4 − 8x^2 + 3 as a local…

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Q: 5. The function f (x) = 2kx³ + 3x² + px – 3 has a local minimum at x = -1 and a point of inflection…

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Q: Find all the critical points of the function f(x, y) = x³ + y³ – 9x2 – 21x – y - 66 and label them…

A: Local Extremum values:              Consider the function f(x,y) .For critical points , fx(x,y)=0…

Q: For the function f(x,y) = 2-x-y+ 3.x + 4 y use the second derivative test to identify any critical…

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Q: construct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be determined.…

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Q: ¥ 5) Find all the critical points of f(x)= = = 2 and determine if they are a relative maximum,…

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Q: Consider f(x) = xlnx on the interval [1,6]. When will the first derivative equal zero? For each…

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Q: 8. Let f(x) = 9x +- Find the critical number(s) and determine whether they are local…

A: fx=9x+1x take the first derivative f'x=ddx9x+1x f'x=ddx9x+ddx1x f'x=9-1x2 take the second derivative…

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Q: 8) State the critical points of the function k(x) = x2 In x2.

A: Given,          The function kx=x2lnx2

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Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

A: The given function is f(x)=2x4-3x3. Find the critical points of f(x)=2x4-3x3 as follows. The…

Q: Find all critical points for the function f(x) = (z² – 4) . %3D

A: To find the critical points of f(x), find the derivative of f(x) and equate it to zero.

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