Let f(x) = 4x – 8a2 + 5x. Find the absolute maximum and the absolute minimum of f on [0, 2].

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Q: What is the relative minimum value of the function f(x, y) = x³ – 3xy + y³ – 2?

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Q: Find all points (x.y) where f(x.y) may have a maximum or minimum. f(x,y) = - 3x + 5xy- 2y² +x+y

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Q: The function f (x, y) = 2x + 3y + 9 - x2 - xy - y2 has a maximum at some point (x, y). Find the…

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Q: 3:- Find the maximum value of the function f(x, y) = x²y on the line x + y = 3.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the global maximum and global minimum of f(x)=x22x in the interval [−1,3].

A: We first find the critical points by solving f'(x)=0

Q: Find the absolute maximum and absolute minimum values of f(x) = ! + In r, on [, e²].

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Q: Find the absolute maximum and minimum values of f(x) = xe-x on the interval [0, 3].

A: Here, f(x) = xe-x on [0,3]   Extreme Value Theorem(EVT):  If a function f is continuous on a closed…

Q: Find the minimum value of f (x) = 7x² – 2x + 4 on the interval (0, 1].

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Q: Find the absolute maximum and absolute minimum of f(x) = = +x² = 15x over the interval [1,5|. - 3.

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

Q: For the function y=x, is x-0 both an inflection point and a local maximum /minimum

A: We need to find first and second derivative for this Question to know about local maximum/minimum…

Q: Let f(x) xe^-x/2 Find the absolute maximum of the value of f on the interval [0,6]

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Q: Find and classify the critical points of the function f(x, y) = 4x²y - 2x - y².

A: We need to determine and classify the critical points of the function: f(x, y)=4x2y-2x-y2.

Q: Find the global maximum and global minimum of f(x)=x√x in the interval [2,3].

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Q: Give an example that: the f'(c) 0 but c is not a local maximum or local minimum.

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Q: ) Because f(-1) and f' changes from negative to positive at x = f(-1) = -7e-1 is a local (and…

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Q: Find the local minimum value of f(x, y) = 4+ x³ + y³ – 5xy.

A: Explanation of the answer is as follows

Q: The function f(x, y) = 2x² + 4y² + 2x³ has a local maximum at the point (0, 0). Select one: O True O…

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Q: Calculate the maximum and minimum of the function f (x,y) = xy subject to the condition x2 + y2 = 1

A: To find the optimal solution, we will use Lagrange multiplier method. The Lagrangian function is…

Q: Let f (x) be the square of the distance from the point (2, 1) to a point (x, 3x + 2) on the line y =…

A: The square of the distance between two points (a, b) and (c, d) = (c - a)2 + (d - b)2

Q: Find the absolute maximum and absolute minimum of f(x) = x – 10VT on the interval [1, 100].

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Q: Find the absolute maximum/minimum value for f(x)=x² – 4x+1 on the interval [(-3, 3] 9.

A: Given: fx=x2-4x+1 and x∈-3,3   The Power law: ddxxn=nxn-1

Q: Find the global maximum and global minimum of f(x)=2x in the interval [−1,3].

A: Given function is Differentiating with respect to x, we get Now, f'(x) =0 for no value of x and…

Q: Find the absolute minimum value of the function   g(x)  = ex/x, x>0

A: The function is gx=exx for x > 0.   Differentiate the function with respect to x.…

Q: 5x f(x) = on the interval[-3,1]. %3| x²+36

A: Given,           fx=5xx2+36 on the interval -3,1

Q: Determine the values of constants a and b so that ƒ(x) = ax2 + bx has an absolute maximum at the…

A: Given:

Q: Find the local minimum value of f(x, y) = 4 + x11 + yll – 11xy.

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Q: Find the absolute minimum of f (æ) = x² – 6 on the interval [1, 2].

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Q: Find the absolute maximum and minimum values of f(x) = x – 2x on the closed interval [0, 2]. -

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Q: Let f (z) = =- 2a? – 4z +1. On the interval -1,3, the absolute maximum value of f is and the…

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Q: Determine the values of constants a, b, c, and d so that f(x) = ax + bx + cx +d has a local maximum…

A: We have to determine the value of a, b, c and d

Q: Let f(x, y) = x² - 4x + y + 9. Find the absolute maximum and absolute minimum of f(x, y) restricted…

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Q: Find the maximum and minimum values of the function f(x, y)-xy subject to g(x, y) = x² + xy + y² =…

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Q: (a) Let f(x) = x³ +*+4. Find the absolute maximum and the absolute minimum of f on the closed…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: The absolute maximum and absolute minimum for the function f(x) = r2 -8x on the interval 0,5 are

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Q: Find the value of x at which the minimum of the function f(x) = x? Occurs.

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Q: Find the absolute maximum and absolute minimum values of the function f(z) = x* – 2x² + 1 on [0, 3].

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Q: Let a, B be positive numbers. Find the absolute maximum value of f(x) = x°(1 – x)*, 0 < x < 1.

A: To find the absolute maximum of the given function.

Q: Find the maximum and minimum value of f (x,y) =x' + 3xy² – 3x² – 3y² +4 = X" - -

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Q: Find the local minimum value of f(x, y) = 4 + x1 + yll – 11xy. 11 11

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Q: Find the absolute maximum value of f(x) = x² – 2x + 12 over the interval [0, 5]

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Q: Find the absolute maximum and the absolute minimum of f(x,y)= 3xy-3x-6y+1 on the closed triangular…

A: Given:- The function is, f(x,y)=3xy-3x-6y+1on the closed triangular region whose vertices are (0,0),…

Q: Find the absolute maximum and minimum values of f(x) = x – 2x on the closed interval [0, 2].

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Q: Find the absolute maximum and minimum values of f on the triangle with vertices (0,0), (3,0), and…

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Q: The function f(x, y) = x² + 4y2- 2x + 8y-1 has a local minimum at the point (-1, 1). Select one: O…

A: We will use first order derivative to find critical point.  If given point is critical point, then…

Q: Find the absolute maximum and the absolute minimum of f(x) = x^3 − 3x^2 on the interval [−1, 3].

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Q: If x² + y² < z < 1, find the maximum and minimum of the function u(x, y, z) = x + y + z

A: We have to find the maximum and minimum of the function.