Find the maximum of y = xa − xb on [0, 1], where 0 < a < b. In particular, find the maximum of y = x5 − x10 on [0, 1].

Q: Find an upper bound for ||L|| where L: R² → R³ with L(x, y) = (2x + y,x + 3y, 3x – 2y) -

A: Here we use the definition of boundedness of a linear operator.

Q: Find the absolute minimum and absolute maximum of the function f(x, y) = x^3 – 2y^3 + 3y + (x – 1)^2…

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Q: Let z = f(x, y) = 5x – x³ + 2xy – y². - Find and classify all the critical point(s) of this…

A: Differentiate the function fx,y=5x-x3+2xy-y2 partially with respect to x and y, to obtain fx and fy.…

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

A: We have to find the critical points for the function f(x,y)=-x2+2y2+6x-8y+5.

Q: Suppose that f(x, y) = x² + y° at which 0 < x, y and 1x + 8y < 7. 1. Absolute minimum of f(x, y) is…

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

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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: Find the absolute maximum and minimum of the function on the given domain. f(x,y) = 5x + 8y on the…

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Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy- 4y. Then: (1,1) is a critical point and f has a…

A: The given function is f(x,y)=6y2+4x2-12xy-4y

Q: Show that the function f(x) = e1/2)[(x-µ)/a}° has a relative maximum at x = µ.

A: fx=e-12x-μσ2 Differentiating with respect to x, we get…

Q: Find the absolute maximum and minimum of the function f(x,y) = 7y + 64x – 3 over the closed region…

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Q: Find the linear approximation L (x) to ƒ (x) = xcosx at a = T.

A: Given that, f(x) = x cosx and we have to find linear approximation L(x) at a = π

Q: Find the smallest value of t > 0 for which h'(t) is a maximum, showing the working.

A: Given time dependent height function h(t) - h(t) = 0.8sinπ2t-1+1.8Differentiating h(t) with respect…

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 3 numbers x, y, and z such that their sum is 32 and P=xy^2z is a maximum.

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Q: Determine the value of the Wronskian W(y1, y2) of y" - 2y + 1 = e2*(x + 1) if x-0.2 by using…

A: Given, y''-2y'+1=e2xx+1. The objective of the problem is to obtain the value of the Wronskian if…

Q: Find the linearization of the function f (x) = x° at æ = 1. L(2) = Using this linearlization, f…

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Q: Find the local minimum value of f(x, y) = 4+ xl+yl1 11æy. -

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Q: 3x4 – 4x3 – 12x² + 18 f(x, y) = 12(1+ 4y²)

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Q: Find the absolute minimum and absolute maximum of f(x, y) = 10 – 2x + 3y osed triangular region with…

A: Given: f(x, y)=10-2x+3yWith vertices (0, 0), (3, 0) and (3, 4)

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

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Q: Find and classify the critical points of f(x,y) = 4r+20² - y²

A: Find and classify the critical points of f(x,y)= 4x+2x2-xy2.

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: + A(- for 0<x< 1, then u attains its maximum in the interval 0 sxs1 either at x=0 or at x= 1.

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Q: Find the absolute maximum and minimum values of the function on the triangular region whose vertices…

A: The given function f(x, y) is a polynomial and therefore, it is continuous and has both maximum and…

Q: find the formula for a function of the form f(t)=at+b/t with a local minimum at (3,3) and a local…

A: For critical values of f(t), f'(t)=0Critical values of f(t) are t=-3 and t=3So we find f'(t) from…

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

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Q: Find a cubic function f (x) = ar + bx2 + cr+ d that has local maximum value of 28 at x = -1 and a…

A: to find:- cubic function f(x), hence the value of a, b, c &amp; d.

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

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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: At (0, 3), the function f (x, y) = 1 – x³ + 6x2 + y2 – 6y has a O a) None of these b) saddle point…

A: The given data is: At 0,3, the function fx,y=1-x3+6x2+y2-6y.

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: Find the two positive x and y such that x+y=60 and xy2 is maximum

A: We have to find x and y in the given question.

Q: At what value of x does the curve y = x(x – a²)(x – b²) have a local maximum?

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Q: Let = f(x,y) = x² -y. Use Euler's method ( with step size h = 1) to approximate the value of y(2) if…

A: The Euler method is a first-order numerical procedure for solving ordinary differential equations…

Q: Find the point at which the function f(r,y) = 2 in z+2 In y attains a maximum subject to the con-…

A: Maxima or minima: For any function f(x), 1) Evaluate f'(x)=0 for critical point. 2) Evaluate f''(x)…

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: Determine the values of constanas a,b,c, and d so that f(x) = ax^3 +bx^2+cx+d has a local maximum at…

A: Given that f(x) = ax3 +bx2 + cx + d has a local maximum at the point (0,0) and a local minimum at…

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: Consider the function y = 3x - C(In x) where C represents a constant. If this function has a local…

A: If any given function f(x) has local maxima or minima at x=a, then the point corresponding to x=a…

Q: Find the absolute maximum and absolute minimum values of the function f(x,y)=x2+y3 on the region…

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Q: 5. Find the absolute maximum and absolute minimum values of f(x, y) = 3xy-3x– 6y+1 on the closed…

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Q: A clamped cubic spline for a function f on 0,3 is given by [1+ax² -2x', S(x) = . [1-2(x-1)+b(x-1)² +…

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Q: For the function f(x,y) = –2x² – 3xy – y? – 3x, does the critical point (6, –9) correspond to a…

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Q: Does the function f(r,y) = e-(z²+y°) achieve an absolute minimum on D= R²? %3D

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

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