Answer:
the maximum value is 7
The minimum value is 0
Step-by-step explanation:
Step One : Interpret the question
The above question can be written like
The Equation
[tex]f(x,y) = 8x^2 +7y^2[/tex]
The diagram of the triangular plate and the bounded lines is shown on the first uploaded image
From the diagram [tex]f(0,0) = 8(0)^2 +7(0)^2 =0[/tex]
[tex]f(1,0) =8(1)^2 + 7(0)^2 = 8[/tex]
[tex]f(0,1) =8(0)^2 + 7(1)^2 = 7[/tex]
Partial differentiation of the equation w.r.x
[tex]A =\frac{\delta f}{\delta x } = 16x[/tex]
Partial differentiation of the equation w.r.y
[tex]B =\frac{\delta f}{\delta y } = 14y[/tex]
Looking at the diagram the maximum value is 7 i.e at (x , y) = (0,1)
The minimum value is 0 i.e (x , y) = (0,0)
