Grade 12Analytical Geometry
Examine for minimum and maximum values of the function f(x,y)=sinx+siny+sin(x+y)
Examine for minimum and maximum values of the function f(x,y)=sinx+siny+sin(x+y)
1 Answer
Arun
Approved Tutor Answer8 Years agoz = sinx + siny + sin(x+y)
to find the maxima, we need
∂z/∂x = 0 and ∂z/∂y = 0
∂z/∂x = cosx + cos(x+y)
∂z/∂y = cosy + cos(x+y)
∂z/dx = 0 when x+y = pi-x
A handy place for this is at (pi/3,pi/3)
z(pi/3,pi/3) = √3/2 + √3/2 + √3/2 = 3√3/2
to find the maxima, we need
∂z/∂x = 0 and ∂z/∂y = 0
∂z/∂x = cosx + cos(x+y)
∂z/∂y = cosy + cos(x+y)
∂z/dx = 0 when x+y = pi-x
A handy place for this is at (pi/3,pi/3)
z(pi/3,pi/3) = √3/2 + √3/2 + √3/2 = 3√3/2
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