x and y are the sides of two squares such that y=x−x2 T
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x and y are the sides of two squares such that y=x−x2. The rate of change of area of the second square with respect to that of the first square is
A.
2x2+3x2+1
B.
3x2+2x2−1
C.
2x2−3x+1
D.
3x2+2x+1
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Right Answer is: C
SOLUTION
Let A=x2 and B=y2=(x−x2)2
∴dBdA=dBdxdAdx=2(x−x2)(1−2x)2x=(1−x)(1−2x)=2x2−3x+1