Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 4x² - 3x + 7y+3y²: x= y= Z=

Q: The function f (x, y) = x² + xy - x + y² + 7y+29 has exactly one critical point. What is it?…

A: Given that the function fx,y =x2 +xy-x+y2+7y+29    .

Q: b) Find and classify all the critical points of f(x, y) = 3x²y + y3 – 3x2 - 3y2 +5. %3D

A: The solution is given as

Q: The critical point of the function f(x) = a – 6x² + 16x + 13 is %3D - (1, –4) (-2,4) (2, 4) (-2, –4)

A: The critical point of the function y=fx is the point where f'x=0. The power rule of differentiation…

Q: Maximize B=xy2​, where x and y are positive numbers such that x+y2=10.

A:

Q: If f(x,y)=xe/2,+37x?y3, then dx²əy³ at (1,1) is equal to

A:

Q: Find the minimum value for p(x) = -x2 – 24x on the interval [-6,-1]. JUSTIFY YOUR ANSWER.

A: px=-x2-24x Differentiating with respect to x, we get p'x=-2x-241=-2x-24 Now to find critical values,…

Q: Find the maximum and minimum values of the 2x3 function f(x,y) = * - 2xy – 5x + 2y² + 4y + – 2xy –…

A:

Q: Find a linear approximation y = f(x) = x5 − 4x² + 4x³ − 12x² + 21x − 6 to the following function at…

A:

Q: a) If y = 3x – 2, x = 3t + 2, and t = 3k – 2, find b) Express y as a function of k ify = 2x + 5, x…

A: Introduction: A function is an expression, rule, or law in mathematics that defines a relationship…

Q: Determine the maximum or minimum value for y = −2(x − 7)(x − 5) and state the value of x for which…

A:

Q: Find the critical numbers of the function f(x)=2x³-3x² - 72x -3 -2 -4 3

A: Explanation of the answer is as follows

Q: Find the maximum value of f(x,y) = 31-x² - y² on the line x + 5y = 26.

A:

Q: If f(x) = x3 – 6x² + 9x + 15 then the minimum value of f(x) over the interval [0, 6] is

A:

Q: If (1,7) is both a critical point and a point of inflection for the function 3 2 f(x)=x²- cx² - 3dx²…

A: fx=x4-cx3-3dx2+5x+5

Q: The function f(x) = 2x³ − 33x² + 108x - 7 has two critical numbers. X = (enter the values separated…

A: Topic- Application of derivatives We are given, f(x)=2x3-33x2+108x-7we know that critical numbers…

Q: One of the following is not a critical point to the function fx, y) = 3x2 - 12x +y+- 2y2- 5. Select…

A: Given function is,       f(x,y)=3x2-12x+y4-2y2-5 We have to find critical points of above function.…

Q: Function f(x) = x4 - 12x3 + 46x2 - 60x + 30 has critical points at:I. x = 1; II. x = 3; III. x = 6.…

A:

Q: 1. The functions fi(x) = 4x, f2(x) = x² + 6x, and fз(x) = 4x² + 12x do not form a linearly…

A: Step 1:  Step 2: Step 3: Step 4: