A) 1/3
B) 1/5
C) 1/8
D) 1/9
Correct Answer: D
Solution :
Given that \[y=2{{x}^{2}}.\] \[|A{{B}^{2}}|={{({{x}_{B}}-{{x}_{A}})}^{2}}+(2x_{B}^{2}-2x_{A}^{2})=5\] \[\Rightarrow \]\[{{({{x}_{B}}-{{x}_{A}})}^{2}}+4{{(x_{B}^{2}-x_{A}^{2})}^{2}}=5\] On differentiating \[w.r.t\,{{x}_{A}}\] and denoting \[\frac{d{{x}_{B}}}{d{{x}_{A}}}=D\] \[2({{x}_{B}}-{{x}_{A}})(D-1)+8(x_{B}^{2}-x_{A}^{2})(2{{x}_{B}}D-2{{x}_{A}})=0\] On putting \[{{x}_{A}}=0\]and \[{{x}_{B}}=1\] \[2(1-0)(D-1)+8(1-0)(2D-0)=0\] \[2D-2+16D=0\]\[\Rightarrow \]\[D=\frac{1}{9}\]You need to login to perform this action.
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