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malfutka [58]
3 years ago
5

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

Mathematics
1 answer:
pickupchik [31]3 years ago
3 0

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

            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 =\frac{\delta f}{\delta x }  = 16x

 Partial differentiation of the equation w.r.y

                          B =\frac{\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)

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