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Let f(x)=x+lnx−xlnx x∈(0,∞) Column 1Column 2Column 3(I)f(x)=0 for some x∈(1,e2)(i)limx→∞f(x)=0(P)f is increasing in (0,1)(II)f′(x)=0 for some x∈(1,e) (ii)limx→∞f(x)=−∞ (Q)f is decreasing in (e,e2)(III)f′(x)=0 for some x∈(0,1) (iii)limx→∞f′(x)=−∞ (R)f′ is increasing in (0,1)(IV)f′′(x)=0 for some x∈(1,e) (iv)limx→∞f′′(x)=0 (S)f′ is decreasing in (e,e2) Which of the following options is the only CORRECT combination? |
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Answer» Let f(x)=x+lnx−xlnx x∈(0,∞) Column 1Column 2Column 3(I)f(x)=0 for some x∈(1,e2)(i)limx→∞f(x)=0(P)f is increasing in (0,1)(II)f′(x)=0 for some x∈(1,e) (ii)limx→∞f(x)=−∞ (Q)f is decreasing in (e,e2)(III)f′(x)=0 for some x∈(0,1) (iii)limx→∞f′(x)=−∞ (R)f′ is increasing in (0,1)(IV)f′′(x)=0 for some x∈(1,e) (iv)limx→∞f′′(x)=0 (S)f′ is decreasing in (e,e2)Which of the following options is the only CORRECT combination? |
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