Question 1 [ variables Given the function of two f(x,y) = −4x² − 6xy-7y²-1. a) Use Lagrange Multipliers to find the extreme value(s) of the function f subject to the constraint -4x+y+6=0. b) [3 Verify that f(x, y) 19 - 17 (4x+3y)² - ( 12 y ²+1) = c) [1] Show that f has maximum and no minimum with the constraint -4x+y+6 = 0.

Q: Answer the following questions about the equation 1 4x³ − y² + ²⁄yz² − x(y − x)e² +1=0. (1) Does the…

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Q: Determine the equation of the quartic function with the following characteristics x-intercepts at x…

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Q: Find all functions y satisfying y" + y" = y' + y. You may use the factor- ization x + x² – x - 1 =…

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Q: Find the maximal value of the function f(x,y)=2x3-y3 on the circle of equation x2+y2=7.

A: We have to find the maximal value of the function  on the circle of equation

Q: A cubie function has rule x) ax+ br + 6. The points (1,4) and (2, 11) lie on the graph of y f().…

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Q: Find and classify the stationary point(s) of the following functions: (a) 1: R³→ R defined by: 1(x)…

A: As per Bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: Let f(x, y) = 2x - 4y + 7. Find the following. (a) f(3,-1) (b) f(-5, 1) (c) f(-5, -4) (d) f(0, 7)

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: Q1 Minimise f(x) = X;² + x;? + 2x3? – x1x2 %3D a) Determine the stationary point and check the…

A: Given, f(x)=x12+x22+2x32-x1x2 a) Stationary point:…

Q: 27. Using x-intercepts and two test points, graph the quartic function: y = (x – 6)²(x + 2)(x – 2)…

A: We have to find the graph

Q: a) If y = 3x – 2, x = 3t + 2, and t = 3k – 2, find b) Express y as a function of k ify = 2x + 5, x…

A: Introduction: A function is an expression, rule, or law in mathematics that defines a relationship…

Q: Find the maximum value attained by the function x² + xy + y² on the set {(x, y) : x² + y² < 2}.

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Q: Find the maximum value of f(x)=−5x2+5x+6 on the interval [−20,20]

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Q: Consider the function f(x, y) = x ^3 + y ^3 + 3xy and the constraint (x − 3)^2 + (y − 3)^2 = 9.…

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Q: Maximize f = 7x₁ + 6x2 + 10x3 subject to 4x1 + 5x2 + 3x3 18 2x1 + 3x2 + x3 0, x3 ≥ 0 If no…

A: The given problem is to find the solution for the linear programming problem with given constraints.

Q: f(x)=√√√√x+2 -9-8-7-6-5-4-3-2-19 -1 -2 -3 -4 -5 -6 -7 -8 -9 1234 hich statement about these two…

A: Given is the function I and a function II as a plot. We have to determine a statement that is common…

Q: Which of these functions has a y-intercept of (0,9) ○ A) ƒ(x) = 9x² + 4x + 2 B) f(x) = 9(x-3) (x +…

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Q: Suppose that x and y are two positive real numbers so that x + y = 10. Maximize the product xy

A: To find the solution of the given problem use the second derivative test. Second derivative test:…

Q: Find the absolute maxima and minima of f(x, y) = xy(18 – 2y - 9x) on the triangle bounded by the…

A: The function f(x,y)=xy(18-2y-9x)=18xy-2xy2-9x2y.  ∂f∂x=18y-2y2-18xy∂f∂y=18x-4xy-9x2 Find the points…

Q: `y = f(x) 1- 1 he graph of the linear function f is shown in th- -plane above. The slope of the…

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Q: If f(x) = v(x - 1)/ (x - 9), then the domain of f is given by the interval A. (1, +00) B. (-3, +3)…

A: The given function is  f(x) = sqrt[(x - 1)/(x2-9)]

Q: (5) Find the domain of the function f(x,y) = ²-In(r+2) 2-y√100-2² - y²

A: Remember the following domain For xy, y≠0 For x, x≥0 For lnx, x&gt;0 Given function…

Q: Find the maximum and minimum values of f(x) = x3 − 6x2 + 8 on the horizontal span of 0 to 10.

A: We're tasked with finding the maximum and minimum values of the function f(x)=x3−6x2+8 over the…

Q: If f(x) = 2 + 3x – 4x², determine the value of the dependent variable f(5) – f(3). Show your work.

A: We can solve the problem by putting the value 5 and 3 in the given function.

Q: 9) Find a linear function of the form f(x) = ax +b that satisfy the conditions A-4) = 8 and (3) - 9.

A: f(x) = ax+bf(-4) = 8→ -4a+b = 8.........................1f(3) = 9→3a +b =…

Q: #5 Given functions Fees=V Zx-1,g)= 3x ²+I find qof 9(x)=D3x²+1 qof and its domain

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Q: What function should be used to minimize the distance between y = x + 5 and the point (3, 1)? O D(æ)…

A: Explanation of the solution is given below...

Q: Let f(r) = x – 8rš. (a) Prove that f has a maximum and minimum value on [0,4]. (b) Find the maximum…

A: Here we have to find the maximum and minimum value of the given function.

Q: 4. The quadratic function f(x) has a turning point at (-3,6). The quadratic y=÷f(x)+3 would have a…

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Q: That  f(x) = -2x,    g(x)= |x + 4|, and h(x)2/x-3. Evalute the functions for the given values of x:…

A: a) Obtain (g o f ) as follows.