Find extremum of value of f(x, y) = 3xy subject to 2x + 3y = 24 minimum of 48 at (6,6) minimum of 54 at (8,3) maximum of 54 at (4,6) maximum of 72 at (6,4) Question 23 (4 points) Find extremum of f(x, y) = x² + 2y²+4xy - 6y. maximum of 45 at (3,3/2) 14 4 % 205 6 9> & 27 ( 7 8 9 0 C

Q: Find all local maximum and minimum points of y = 2 + 3x − x³ by the second derivative test.

A: y = 2 + 3x - x3    => y' = dy/dx = 3 - 3x2 = 0 (set)                => 3(1 - x2) = 0…

Q: Determines the speed at which the two cars approach or move away from each other 0.5 hours later.…

A: The distance function d between two cars is given, we have to find at time t = 0.5 whether the car…

Q: 2. F(x, у) %3D — (у i-2x) y2

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: If APOR ATSR, find SR. 2X-1 2r-1 P. 60 4x- 26 R 38 1/x-3

A: Given, ∆PQR ~ ∆TSR  We have to find the value of SR

Q: 3x10 + 3a5 + 5æ² + 7. What particular solution that satisfies Suppose f'(x) 455 -? 66 f(1)

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Q: If f(x, y) = %3D

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Q: Find the value of fa and fy at (1, -1) when 4 f(x,y) =+5x²+3y². xy 1. 1- = 9, f = = -7 2 2. f= = =…

A: use partial differentiation for finding the solution.

Q: The function of two variables f(x,y)=(y-2) x^2-y^2 has: A local min. at (0, 0) A saddle point at (0,…

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Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: The weekly revenue realized by a company is approximated by the revenue function R(x, y) = 550x +…

A: The weekly revenue realized by a company is approximated by the revenue function R(x, y) = 550x +…

Q: 8) Suppose you are at the point (2, 1, 82) on the hill given by f(x,y) = 100-4x²-2y (where the z…

A: The objective of this question is to understand the concept of directional derivatives and gradient…

Q: 6. For f(x, y) = x²exy Find fx (2,1) {needs product rule}

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Q: 4) f (x) = fiod the interval Cs) on which %3D graph of f(x) is Concave up (if any)

A:

Q: Find y'. 4) y = (5x3 + 5)(5×7 .7) A) 250x9 + 175x6 - 105x2 C) 20x9 + 175x6 - 105x2 B) 250x9 + 175x6…

A: The function is given by y = 5x3+55x7-7 To evaluate: The expression of y'

Q: 15. For f (x) = x ^ 3 -12x + 10 the interval where f (x) is concave downward is: A. (0, ) b. (-00,…

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Q: It is the case that (x4 – y4)", where A=7 and n > 0 is a parameter, simplifies to x" – y". Please,…

A:

Q: Can the level surface x^2 + y^2 + z^2 − 5 = 0 be expressed as the graph of a function f(x, y)?

A: Level surface isif possible then we have to express as it the graph of a function f(x, y).

Q: For what values of the parameter 'a' does the function f (x)=x³+3(a - 7)x² +3(a? -9)x - 1.have a…

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Q: 8) Suppose you are at the point (2, 1, 82) on the hill given by f(x,y) = 100-4x²-2y (where the z…

A: The objective of the question is to determine the direction and rate of change of the elevation of a…

Q: Help 18 cubic function whose graph has horizontal tangents at (-2,6) and (2₁0). {Y= ax ³ + bx²²…

A: Let's solve.

Q: Given the 3 functions. F(x,y) = 2x+y. G(x,y) = x^2 + y, and H(x,y) = (x^3 + y^3) / (x^2 + y^2)…

A: Given: Fx,y=2x+y, Gx,y=x2+y, Hx,y=x3+y3x2+y2To classify each of the above given function as linear,…

Q: Find the value of fr and fy at (1,-1) when 4 +5x² + 3y². xy f(x, y) =

A: Given: fx,y=4xy+5x2+3y2We need to find fx and fy at 1,-1.

Q: 6. Find the local maximum and minimum values of f (x) = 9 + 9x² – 6x³ using both the First and/or…

A: In this question we have to find local maximum and minimum values of the function.