if y= x, [x(ax+bx)- ax^2]/(ax+bx)^2= [ax^2+ bx^2- ax^2]/(a+b)^2x^2= b/(a+b)^2 and [x(ax+by)- bxy]/(ax+by)^2= a/(a+b)^2 so dP= (b+ a)/(a+b)^2= 1/(a+b)dx. Your definition of "marginal profit" might be that 1/(a+b).
At what point? the tangent plane is different at each point. The gradient is perpendicular to the surface at (x, y, z). Do you know how to find the plane with a given normal vector and point?find the equation of the horizontal plane that is tangent to the graph
z= G(x,y)= x^2 -4xy - 2y^2 +12x - 12y -1
how do u do this question with 3 d graph?
i am right now please help