Multiple Choice Questions on Given function f x y 4x2 6y2 8x 4y 8 find the optimal value of f x y ........ for NDA Exam Preparation

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Multiple Choice Questions

Given function f x y 4x2 6y2 8x 4y 8 find the optimal value of f x y ........

Mathematics (NDA) Diffrentiation
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    Given function f(x,y) =4x2  +6y2 -8x -4y +8 ,find the optimal value of f(x,y)?

    1/3

    Incorrect Answer

    10/3

    Correct Answer

    5/3

    Incorrect Answer

    2/3

    Incorrect Answer
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    Explanation:

    df/dx =8x -8

    df/dx  =0

    X=1

    df/dy  =12y -4

    df /dy =0

    12y  -4 =0

    Y=1/3

    Point (1,1/3)

    df2/dx2 =8 >0  at point(1,1/3)  minima

    df2  /dy2 =12

    optimal minimum value (1,1/3)

    f(1,1/3)=4 × 1 +6 ×  1/32  -8×  1  -4  × 1 +8   

    =10/3

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