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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)

Grade:12

1 Answers

Arun
25758 Points
4 years ago
z = 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

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