InterviewSolution
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InterviewSolution
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The value of the parameter a such that the area bounded by `y=a^(2)x^(2)+ax+1,` coordinate axes, and the line x=1 attains its least value is equal toA. `(1)/(4)` sq. unitsB. `-(1)/(2)` sq. unitsC. `(3)/(4)` sq. unitsD. `-1` sq. units |
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Answer» Correct Answer - C `a^(2)x^(2)+ax+1` is clearly positive for all real values of x, Area under consideration `A=overset(1)underset(0)int(a^(2)x^(2)+ax +1)dx` `=(a^(2))/(3)+(a)/(2)+1` `=(1)/(6)(2a^(2)+3a+6)` `=(1)/(6)(2(a^(2)+(3)/(2)a+(9)/(16))+6-(18)/(16))` `=(1)/(6)(2(a+(3)/(4))^(2)+(39)/(8))`, which is clearly minimum for `a=-(3)/(4).` |
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