use lagrange multipliers to find the largest and smallest values of -y^2 + 2xy - 2x^2 with constraint of x^2 + y^2 <= 1

Q: Find two positive integers whose sum is 16 and the sum of whose squares is minimum

A: Given sum of two numbers are 16. Let first number be x and second number=16-x. Now, sum of squares…

Q: Find the vertex of the parabola Y= 6X^2.+24X + 18 O (6, 2) O (2, 6) O (2,-6) O (2, 6)

A: We have to find

Q: Determine the vertex- f( x)= x^2 +4x +3 O (2-1) (-2, -1) O (3,-1) O (1,-2)

A: given equation of parabola f(x)=x2+4x+3 we know vertex is the maximum of minimum of a parabola,…

Q: Find the line y = mx + b that best approximates the data points (0, 0), (1, 2), (2, 1) in the sense…

A:

Q: Suppose the cost per hour incurred in operating a cruise ship is 5a + b^4v^3 dollars per hour, where…

A: Step:-1 Note:-  your cost expression is not clear here as it can be 5a+b4v3   or   5a+b4v3 , So i am…

Q: find the local maximum value of the function xy-x^2-y^2-2x-2y+4

A: The given function

Q: a^2+b^2+c^2 = 2 then find minimum value of 3a+4b+5c

A:

Q: Find domain and range of the * function y = Vx2 – 4x

A: To find the domain and range of  y=√(x²-4x)

Q: Is the function R(q)=1/q^2(q^2+5)^2 quadratic? If so, write the function in the form R(q)=aq^2+b⁢q+c…

A: We have to distribute (q^2+5)^2 first using (a+b)^2 formula.

Q: Determine two positive numbers whose product is 4 such that the sum of their squares is minimum.

A:

Q: Suppose thatf(x) = (x+ 5)^3(x-2)^4. Find the x-coordinates of all points of inflection

A: To find- x-coordinates  of all points of inflection.

Q: Find the value of x that results in a maximum value of y if -2=x^2+y^2-4x+4y?

A: The given equation is -2=x2+y2-4x+4y. To find the value of x that results in a maximum value of y,…

Q: During sales hour in a supermarket, Cynthia measures her urgency from buying a bags of candies and y…

A: The given problem is to find the maximum number of bags of chocolates and candies bought with given…

Q: Find the maximum and minimum points for y = x^5 -5x^3 -20x – 2

A:

Q: Find the value of c such that the exp k^(2)+13k+c

A:

Q: Suppose x and y are positive integers such that the sum of x^2 and y is 10x. Find the values of x…

A: Given x^2+y=10x.From there find y.