A) 24
B) \[6\sqrt{3}\]
C) \[-6\sqrt{3}\]
D) - 12
Correct Answer: A
Solution :
\[y=-\lambda \left[ {{x}^{2}}-x-\frac{8}{\lambda } \right]\] \[=-\lambda \left[ {{\left( x-\frac{1}{2} \right)}^{2}}-\frac{1}{4}-\frac{8}{\lambda } \right]\] \[=-\lambda {{\left( x-\frac{1}{2} \right)}^{2}}-\frac{\lambda }{4}+8\] \[y\] is maximum when\[x=\frac{1}{2}\] \[i.e.\] \[\frac{\lambda }{4}+8=14\] or \[\lambda =24\]
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