Let m and n be positive integers and `x,y gt 0 and x+y =k,` where `k` is constant. Let `f (x,y) = x ^(m)y ^(n),` then: (a) `f (x,y) ` is maximum when `x= (mk)/(m+n)` (b) `f (x,y)` is maximuim where `x =y` (c) maximum value of `f (x,y)` is `(m^(n)n ^(m) k ^(m+n))/((m+n)^(m+n))` (d) maximum value of `f (x,y)` is `(k ^(m+n) m ^(m)n ^(n))/((m+n)^(m+n))`

Options

A. `f (x,y) ` is maximum when `x= (mk)/(m+n)`
B. `f (x,y)` is maximuim where `x =y`
C. maximum value of `f (x,y) is (m^(n)n ^(m) k ^(m+n))/((m+n)^(m+n))`
D. maximum vlaue of `f (x,y) is (k ^(m+n) m ^(m)n ^(n))/((m+n)^(m+n))`

Answer

A, D