Question:medium

Consider the function \[ f:(0,\infty)\to(-\infty,\infty) \] given by \[ f(x)=\sqrt{x}\log_e(x)-x+1 \] Then which one of the following statements is TRUE?

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If: \[ f'(x) \] changes from positive to negative at a point, then the function has a local maximum there.

Updated On: May 20, 2026

The derivative of the function \(f\) is decreasing in the interval \((0,1)\)
The function \(f\) has a local maximum at some point \(a \in (0,\infty)\)
The function \(f\) has a local minimum at some point \(b \in (0,\infty)\)
The function \(f\) has neither a point of local maximum nor a point of local minimum in \((0,\infty)\)

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The Correct Option is B

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