For what value of x does the function f(x) = x³ – 2x² + x- 11 have a relative maximum? А) 1/3 В) 1 -1/3

Q: Suppose that f(x, y) = x² − xy + y² − 5x + 5y with x² + y² ≤ 25. 1. Absolute minimum of f(x, y) is…

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Q: Find the maximum of y = xa − xb on [0, 1], where 0 < a < b. In particular, find the maximum of…

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Q: Show that the function z = f (x,y) = x³ – 3x² – 4y² + 2 has one saddle point and one maximum point.…

A: Given

Q: Find the point where the maximum value of f(x, y) = xy subject to y = 33 – x² occurs. (x, y, z) =

A: (x,y,z) = (√11,  22,  22√11)  The detailed solution is as follows below:

Q: Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the…

A: We have, To find the critical point, we have to take the partial derivative of the function, and…

Q: Find the linearization of f(x) = (1+ x)20 at x = 0. Use it to approximate (1.001)20.

A:

Q: True or False: The linear function y = mx + b, where m # 0 has no maximum value on any open…

A: The answer is True.

Q: At waht x does f(x) have a local(relative) maximum?

A: A function f(x) is defined for x values there are local maxima and local minima in the given curve.

Q: What value of a makes ƒ(x) = x2 + (a/x) have a. a local minimum at x = 2? b. a point of inflection…

A: Given,

Q: 8, find the the function maximum value of +(x, y,Z) 2179`x+ 2y -12+7 subJect to Constrain t+3 +2² =…

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Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

A: The given function is: f(x,y)=e-4x2-4y2-x+2y Here,…

Q: 1.Test the function def ined by f(x.y)=xlnx- ylnx for its homogeneity. If it is homogeneous, give…

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Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 2x + 9y < 8. 1. Absolute minimum of f(x, y) is…

A:

Q: Find the absolute maximum and minimum of f(x, y) = 3z +y within the domain z² +y? < 4.

A: Use lagrange multiplier.

Q: Determine two functions, defined on the interval  ( − ∞ , ∞ ) , whose Wronskian is given by  W ( f 1…

A: To determine two functions having the prescribed Wronskian and decide on their linear independence

Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 4x + 8y < 8. 1. Absolute minimum of f(x, y) is…

A:

Q: Suppose that f(x, y) = x² + y? at which 0 < x, y and 5x + 6y < 8. 1. Absolute minimum of f(x, y) is…

A: This question is related to linear programming, we will solve it using given information.

Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 2 at x = −2 and a…

A: f(x) = ax3 + bx2 + cx + d f(x) = 3ax2 + 2bx + c Now, f(x) = 0  at x = -2, 1 Hence , roots of above…

Q: Find the (x, y) critical point (s) of the function f(x, y) = 2x³ + y² − 9x² − 4y + 12x − 2 . Then…

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Q: How can we minimize the error of an approximation in a linear approximation at the point (a. ƒ (a))?…

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Q: 8. If f(x) = 4 sin x + 6 and g(x) = 3x + 5, what is the maximum value of f(g(x))?

A: Solution is given below

Q: Find the quadratic function f (x) = ax2 + bx + c that goes through (0, 1) and has a local minimum at…

A: Given: The quadratic function fx=ax2+bx+cpasses through the point 0,1 and has local minimum at 1,-1,…

Q: Find the local linear approximation of f(x)= at 2+ x xo = 2, where Ax = x – 2. NOTE: Enter the exact…

A: while finding out the local linear approximation of any function f(x), what we do is to determine…

Q: Find the relative maximum or minimum value (if any) of f(x, y) = (x2 + y)ey/2

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Q: Suppose that f(x, y, z) = 2x + 5y + 4z at which a2 + y? + z2 < 12. 1. Absolute minimum of f(x, y, z)…

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Q: Find the maximum value of x if f(x)=5 sin x – Using Quadratic Interpolation with a relative error of…

A: Given: If f(x)=5sin x-x610, find the largest value of x. Using Quadratic Interpolation with a 1%…

Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 4x + 7y < 9. 1. Absolute minimum of f(x, y) is…

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Q: Find the linear approximation to f(x) = (x+2) at 0 and use it to approximate (2.001)

A: Given :           f(x) = (x + 2)5 at 0 To find :             The linear approximation of f(x)…

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) = y - 8ry + 2x? – 3y + 4x - 23 . Find all critical values for this function and…

A: If rt - s2 &gt; 0 and r&gt;0 then the function is minimum at point ( a,b) If (rt - s2) &lt;0 and…

Q: Find all points (x,y) where f(x.y) has a possible relative maximum or minimum. f(x.y) = x* - 32xy +…

A: Solution:Given thatfx,y=x4 -32xy+8y2-10we have to find all points x,y where fx,y has a possible…

Q: Suppose that t hours after the injection of x milligrams of adrenalin the response is R units, and…

A: The response after t hours of x mg of adrenalin is R=te-t(c-x)x where c is any constant. We want…

Q: Find absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

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Q: Calculate all of the critical points of the function: f(x, y) = x4 + 64xy² + 32y4 is a relative…

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Q: Find a multivariable function f(x, t) that satisfies the Black-Scholes equation: ft = f - xfx -…

A: f(x,t)=etlog(x) satisfies Black-Scholes equation: ft = f - xfx - x2fxx

Q: Find constants a and b in the function f(x): ar In(x) such that f() = 1 and the function function…

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Q: What value of a makes ƒ(x) = x2 + (a/x)have a local minimum at x = 2?

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Q: Suppose that the function f(x, y) = x°y+ax – 8y + 5 has a critical point at (2, –2). What must the…

A: For a function of two variables, f(x, y), a critical point is defined to be a point at which both of…

Q: Find the maximum and minimum attained by f(x, y) = 3xy + 2x + 3y in x2 + y < 1. You must use…

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Q: Show that the function z = f(x,y) = x³ – 3x² – 4y² + 2 has one saddle point and one maximum point.…

A: Given a function in two variablesz=fx,y=x3-3x2-4y2+2

Q: Suppose that f(x, y) = x² + y at which 0 < x, y and 3x + 9y < 7. 1. Absolute minimum of f(x, y) is…

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Q: Suppose that f(x, y) = x² – ry + y² – 5x + 5y with x² + y? < 52. 1. Absolute minimum of f(x, y) is…

A:

Q: Show that the linearization of f(x) = (1 + x)k at x = 0 is L(x) = 1+ kx.

A: We need a linear approximation formula for f(x).

Q: 2 f(x, y) = x² + 3xy

A:

Q: The function f(x, y) = -2x² + 4y² - 11 has a local minimum at the point (0, 0). Select one: True…

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Q: what is the maximum of the function g(x,y) = (x2 + y - 11)2 + (x + y2 - 7)2 over the region 0 ≤ x ≤…

A: The given function gx, y=x2+y-112+x+y2-72 over the region 0≤x≤5 and 0≤y≤5. The required partial…

Q: = 1 Find the minimum value of f(x, y, z) = 3x − y − 3z subject to x² + 2z² - - and x + y -z = 0.

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Q: Find the point where the maximum value of f(x, y) = xy subject to x + 5y = 74 occurs. (x, y, z) = |

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Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 5x + 6y < 7. 1. Absolute minimum of f(x, y) is…

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Q: Find the maximum value of J (x) f(x) = V1 + x² on the indicated interval. [0,2]

A: