If ƒx(a, b) = ƒy(a, b) = 0, must ƒ have a local maximum or minimum value at (a, b)? Give reasons for your answer.

Q: Find all critical points of f(x,y) = 1/x - 1/y + xy and classify each as a relative minimum,…

A: We use second order partial derivative test to find relative maximum and minimum, saddle point

Q: What is the relative minimum value of the function f(x, y) = x³ – 3xy + y³ – 2?

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Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

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Q: Find the quadratic function f(x) = ax + bx +c that goes through (2,0) and has a local minimum at (0,…

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Q: Determine whether the following statement is true or false, and explain why. The cosine function has…

A: It is given that The cosine function has an infinite number of critical points where an absolute…

Q: Minimize ?=?+3?+10 subject to:  2?+4?≥8  4?+3?≥12  ?,?≥0 Corner points at…

A: The objective function is given as, Zx,y=x+3y+10 Subjected to the following constraints,…

Q: Determine whether the following statement is true or false, and explain why. For a function z = ƒ(x,…

A: Let f(x, y) and its first and second derivatives are continuous at (a, b) and that fxa, b=fya, b=0,…

Q: Find the orthogonal trajectories to the family of curves: x² = C-v'(ln y² –1).

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Q: Find the maximum rate of change of the function f(x, y) 4y at the point (5,1)

A: Given f(x, y) at (5, 1)  We have to find find the maximum rate of f(x, y) at (5, 1) by using the…

Q: Find the maximum rate of change of the function f(x, y) : 4y4 at the point (1,3)

A: We will solve the problem

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: Find a point c satisfying the conclusion of the MVT for the given function and interval: y = ex − x,…

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Q: i) Find the orthogonal trajectories of the family of curves: y : 1+ x?

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems

Q: What is the isogonal trajectories cutting at angle of 0= arctan 4 to the family of curves whose…

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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: Find the maximum rate of change of the following function at the given point. f(x, y, z) = x² + 5xz…

A: To Determine: find the maximum rate of change of the following function at the given point . Given:…

Q: Find constants a and b so that the minimum for the parabola f(x) = x- + ax + bis at the point (5,…

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Q: Calculate all of the critical points of the function: f(x, y) = x² xy + 2y? %3| is a relative…

A: f(x,y)  = x^2-xy+2y^2 f'(x)= 2x-y f'(y)= 4y-x for critical points : f'(x)=0 then 2x-y=0  f'(y)=0…

Q: Find the coordinates of the points where the gradient is zero on the curve y = x + . Establish…

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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: Let f(x) = S* A et dt. At what value of x, f(x) has a minimum? Select one: 4 -2 no value of x

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Q: Find the orthogonal trajectories of the one parameter family of curves ex+e-y=c

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Q: Find the orthogonal trajectories for the families of curves y+x^2 = w where w is a parameter

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Q: Find the orthogonal trajectories of the family of 1 curves Y= X + k

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Q: What is (V and find the relative minimum point as indicated by the black dot on the graph at the…

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Q: Show that f(x,y) = 1-x* - y* has a relative maximum, even though D in the theorem is 0. The critical…

A: Given : f(x, y) = 1 - x⁴ - y⁴

Q: Find the orthogonal trajectories for the family of curves. (Enter your solution in the form F(x, y)…

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Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

Q: Find the orthogonal trajectories to the family of curves: r=c- (in y -1).

A: Orthogonal trajectories can be find in the following way: (i) differentiate given family of curves,…

Q: Suppose (2,1) is a critical point of a function f (x,y)· If D=4x – 5y and f=x+y, XX classify the…

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Q: 5. Find the orthogonal trajectories for a family of circles tangent to the at y-axis.

A: Here we have to find the orthogonal trajectories for a family of a circle tangent to the x-axis and…

Q: Find the maximum rate of change of the function f(x, y) 3y5 x at the point (3,4)

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Q: (a) False. For example, x = 0 is a critical point off (x) = x 3 but is neither a local minimum nor a…

A: Given:fx=x3 ,  x=0 is a critical point

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 an equation in the form y = ax³ + bx² + cx + d_whose graph has a critical point that is a local…

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Q: Calculate all of the critical points of the function: 6 6 f(x, y) = xy + + - is a relative minimum v

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Q: 2. Find the orthogonal trajectories of the family of curves x2 + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: Find the critical points of the function f(x, y) = y² + x?y+x² – 2y and use Second Derivative Test…

A: Follow the steps below to yield the result . Calculate . Find the critical point by solving the…

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

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Q: 5. Find the orthogonal trajectories for a family of circles tangent to the y - axis and centers at x…

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Q: Calculate all of the critical points of the function: f(x, y) = x² + 9y² + 6 is a relative minimum

A: Given function is f(x,y)= x^2 + 9y^2 +6

Q: Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) y = 19k

A: The objective of the question is find the orthogonal trajectories of the family of the curves.

Q: Find the orthogonal trajectories of the family of curves x3y-xy3=c where c is constant

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Q: Find the point where the minimum value of f(x, y) = xy subject to y = 90 – x occurs.

A: Find the point where the function f(x,y)=xy subject to y=90-x2 attains its minimum value.

Q: Find the critical point of ƒ(x, y) = xy + 2x - ln x2y in the open first quadrant (x &gt;0, y&gt;0)…

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Q: (b) Sketch the graph of a function that has a local maximum at 3 and is continuous but not…

A: To sketch the graph of the function which is local maxima at 3 and not differentiable at 3

Q: At a point where y' = 0, if y changes from positive to negative as x increases, Ay is maximum By is…

A: We want to find true option.

Q: Once again, a particle travels at velocity t – 1 at time t. Divide the interval 0, 2 into 2k…

A: A particle travels at the velocity t-1 at time t.  We now divide the interval 0, 2 into 2k intervals…