What is the graphic for #f(x,y)=x y^(x/y)=C_0# ? Calculus Applications of Derivatives Solving Optimization Problems 1 Answer Cesareo R. Nov 4, 2016 See below. Explanation: Making #x = lambda y# and substituting in #f(x,y)=x y^(x/y)=c_0# we have #f(lambda y,y)=lambda y y^lambda=lambda y^(lambda+1)=c_0# so #y(lambda)=(c_0/lambda)^(1/(lambda+1))# and also #x(lambda)=lambda (c_0/lambda)^(1/(lambda+1))# so we can generate #x,y# pairs obeying the condition. #f(x,y)=x y^(x/y)=c_0# Attached a plot of #x(lambda),y(lambda)# for #lambda in [0.1,3]# Answer link Related questions How do you find two numbers whose difference is 100 and whose product is a maximum? How do you find the dimensions of a rectangle whose area is 100 square meters and whose... How do you find the points on the ellipse #4x^2+y^2=4# that are farthest from the point #(1,0)#? How do you find the dimensions of the rectangle with largest area that can be inscribed in a... Question #517b1 Let's say I have $480 to fence in a rectangular garden. The fencing for the north and south... How do you find the volume of the largest right circular cone that can be inscribed in a sphere... How do you find the dimensions of a rectangular box that has the largest volume and surface area... What are the dimensions of a box that will use the minimum amount of materials, if the firm... How do you find the dimensions that minimize the amount of cardboard used if a cardboard box... See all questions in Solving Optimization Problems Impact of this question 1283 views around the world You can reuse this answer Creative Commons License