Match the following Column - 1 with Column - 2 List - I List - II (A) f ( x ) = x 2 lo g e x (p) f (x) has one point of minima (B) f ( x ) = x lo g e x (q) f (x) has one point of maxima (C) f ( x

Question

Match the following Column - 1 with Column - 2

List - I	List - II
(A) $f (x) = x^{2} lo g_{e} x$	(p) f (x) has one point of minima
(B) $f (x) = x lo g_{e} x$	(q) f (x) has one point of maxima
(C) $f (x) = \frac{l o g _{e} x}{x}$	(r) f (x) increases in 0, e)
(D) $f (x) = x^{- x}$	(s) f (x) decreases in (0, 1/e)

TestHub · Accepted Answer

(A) For f ( x ) = x 2 lo g x , we have f ′ ( x ) = x ( 2 lo g x + 1 ) = 0 , which implies x = e ​ 1 ​ . This is the point of minima as the derivative changes sign from negative to positive. Also, the function decreases in ( 0 , e ​ 1 ​ ) .

Mathematics - Application of Derivative Question with Solution | TestHub

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