Question

Find the absolute maximum and minimum of the function on the given domain. f (x comma y )equals 8 x squared plus 7 y squared on the closed triangular plate bounded by the lines x equals 0 comma y equals 0 comma y plus 2 x equals 2 in the first quadrant

Answer 1

the maximum value is 7

The minimum value is 0

Explanation:

Step One : Interpret the question

The above question can be written like

The Equation

`f(x,y) = 8x^2 +7y^2`

The diagram of the triangular plate and the bounded lines is shown on the first uploaded image

From the diagram
`f(0,0) = 8(0)^2 +7(0)^2 =0`

`f(1,0) =8(1)^2 + 7(0)^2 = 8`

`f(0,1) =8(0)^2 + 7(1)^2 = 7`

Partial differentiation of the equation w.r.x

`A =(\delta f)/(\delta x ) = 16x`

Partial differentiation of the equation w.r.y

`B =(\delta f)/(\delta y ) = 14y`

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)