Find the Maximum and Minimum values of f(x, y,z) x +3y subject to the constrains x'+4y +z-36.

Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

Q: If f(x, y, z) = 16xy – 4yz – 4zx + 3, then the first order partial derivative fz = - - (4y + 4x) - –…

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Q: 4. Find the points on x² + y² + z² = 25, %3D where the temperature T(x, y, z) = x² + 4y² + 9z², is…

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Q: Show that f(x, y) = x^2 + y^2 − 2xy + 4 has infinite number of critical points and that D = 0 at…

A: Given that      f(x,y) = x2+y2 -2xy+4 has infinite number of critical points and D= 0 at each one.…

Q: Expand x'y + 3y - 4 about the point (1, -2) by Taylor' s theorem.

A: Let, the given function be fx,y=x2y+3y-4 and the given point is 1,-2

Q: Find the maximum rate of change of f(x,y) =x²y+ /y at the point (1,1). In what direction does it…

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Q: Find the value of ∂z/∂x at the point (1, 1, 1) if the equation xy + z3x - 2yz = 0 defines z as a…

A: Given, the equation xy + z3x – 2yz = 0, defines z as a function of two independent variables x and y…

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Q: 2. Find a function f(x, y) which is NOT linear in either a or y and for which the tangent plane at…

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Q: Find the value of at the point (1,1,1) if the equation 3xy +z°x-2yz = 2 defines z as a function of…

A: First do the partial differential in both the sides and then separate ∂z∂x and then put the value…

Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy² = 2 (C- cos x) O…

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Q: Obtain the orthogonal trajectories of xy = C and compute for the positive value of y at the point…

A: Solution

Q: Find the maximum rate of change of f (x, y) = xln /x2 + y2 at (1,2) and direction in which it…

A: To find the maximum rate of change of fx,y=xlnx2+y2 at 1,2 and direction in which it occurs.  First,…

Q: If f(x, y, z) = 12ry - 2yz - 6zx + 7, then the first order partial derivative f = O - (2y – 6x) (2y…

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Q: Solve for the partial derivative with respect to x, y and z f(x, y, z) = x²y + xy² + 2xyz

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Q: Find the first partial derivatives with respect to x and y of f(x,y) = (4x-y)/(4x+y) at the point…

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Q: Find the first partial derivatives of 3x - y f(x, y) = 3x + Y at the point (x, y) = (4, 4). af (4,…

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Q: Compute the partial derivative fxxyz for f(x, y, z) = cos(cos(x3 + z2 )) + x2 ln(y2 + z2 ).

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs…

A: Consider the function: fx,y,z=xlnyz Differentiating with respect to “x” then,…

Q: (2) Let f(x, y, z) = xy + yz + x²z². What is the maximum rate of change of f at (1,2, 3)?

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Q: Let f (x, y) = y^2x − yx^2 + xy.  (a) Show that the critical points (x, y) satisfy the equations y(y…

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Q: Find the partial derivative of f(x,y) with respect to y at the point (3,2) f(x,y) = ln(x^2y-xy^2)

A: A partial derivative of a function of several variables is its derivative with respect to one of…

Q: Find all the second partial derivatives forf (x, y) = x³y5 + 2x*y.

A: All the solutions are given below.

Q: Find the maximum and minimum values attained by f(x, y, z) = 2xyz on the unit ball x2 + y2 + z2 < 1.…

A: fx,y,z=2xyz on the unit ball x2+y2+z2≤1 gx,y,z=x2+y2+z2-1 ∇f=∂f∂x,∂f∂y,∂f∂z ∇g=2yz,2xz,2yx…

Q: derivative

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Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy²= 2 (C- cos x) O y…

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

Q: Find and classify all critical points of f(x,y)%3Dx'+y-4xy+1.

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Q: Show that the Second Derivative Test is inconclusive when applied to the following function at…

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Q: Suppose f(x, y, z) = xy cos z.Compute the partial derivative of f with respect to the variable y at…

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Q: Find the value of at the point (1, 3, 1) if the equation 6xz + ylnx – 5x² – 1 = 0 defines x as a…

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Q: A heat-seeking particle is located at the point (2, −2) on a metal plate whose temperature at (x,y)…

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 3z) at the point (– 2, – 3, – 6). - -

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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: 1. Find the directional derivative of g(r, y, 2) = :2 - zy + 2y? at P = (2,1, -3) in the direction…

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Q: Show that (x, y, z) = xy + y² + 22 has no local extrema by showing that its unique critical point is…

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 2y + 3z) at the point (−9, 6, 2) and the…

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Q: Integrate f(x,y, z) = 2x – 3y² – 2z+3 over the line segment from the origin to (1, 1, 1) and over…

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Q: Find the partial derivative of u = x^2 + y^2 + z^2 - 4xyz

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Q: Find the first partial derivatives with respect to x, y, and z.…

A: The given function is f(x, y, z) = 3x2y − 5xyz + 10yz2

Q: Find the linearization of ƒ(x) = 2x at x = 0. Then round its coefficients to two decimal places.

A: Given function is,

Q: Find the maximum rate of change of f(x, y, z) = tan(7x + 3y + 6z) at the point (4, – 5, 2).

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Q: (b) Form the partial equation by eliminating function f from z = f(x?

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Q: (b) Show that the function defined by xy √√√²+y² f(x, y) 0 if (x, y) = (0,0) is not differentiable…

A: We have to show that the function defined by…

Q: Find the first partial derivatives of 3x – 2y f(x, y) = at the point (x, y) = (1,4). 3x + 2y af…

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

Q: Make the curve y = ax4 + bx³ + cx² + dx + e pass through the point (1, -8) be tangent to the line y=…

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Q: Solve for the partial derivative with respect to x, y and z f(x,y,z) = x²y + xy² + 2xyz

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