AP EAMCET2015MathematicsApplication of Derivatives

If x^2+y^2=25 , then ₅[ (3 x+4 y)] is

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Correct answer

A. 2

Step-by-step solution

Given x^2+y^2=25 aligned & y= 25-x^2 & Let z=3 x+4 y & z=3 x+4 25-x^2 aligned Differentiating w.r.t. x , we get d z d x =3+ 4 2 25-x^2 (-2 x) For maxima put d z d x =0 aligned & 3= 4 x 25-x^2 & 3 25-x^2 =4 x & 9 (25-x^2 )=16 x^2 & 9 25-9 x^2=16 x^2 & 9 25=(16+9) x^2 & x^2=9 & x=3 & y= 25-x^2 y=4 aligned Now, z=3 x+4 y=3(3)+4(4)=25 So, ₅[ (3 x+4 y)]= ₅[ (z)] aligned & = ₅[(25)]= ₅(5)^2 & =2 ₅ 5=2 aligned

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