Let f(x)=x+log_ex-xlog_ex ,x(0,oo)dotColumn 1 contains information | Filo

class 12

Math

Calculus

Application of Derivatives

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150

Let f(x)=x+log_ex-xlog_ex ,x(0,oo)dotColumn 1 contains information about zeros of f^(prime)(x)f^(prime)(x)a n df^(x)dotColumn 2 contains information about the limiting behaviour of f^(prime)(x)f^(prime)(x)a n df^(x)at infinity.Column 2 contains information about the increasing/decreasing nature of f(x)a n df^(prime)(x)dotColumn I, Column 2, Column 3I, f(x)=0forsom ex(l , e^2), (i), ("lim")_("x"vecoo"")f^(prime)(x)=0, (P), fis increasing in (0,1)II, f'(x)=0forsom ex(l , e), (ii), ("lim")_("x"vecoo"")f^(x)=-oo, (Q), fis decreasing in (e ,e^2)III, f'(x)=0forsom ex(0,1), , ("lim")_("x"vecoo"")f^(prime)(x)=-oo, (R), fis increasing in (0,1)IV, f^(' '(x))=0forsom ex(1, e), , ("lim")_("x"vecoo"")f^prime^'(x)=0, (S), fis decreasing in (e , e^2)Which of the following options is the only CORRECT combination?(I) (ii) (P) (b) (IV) (iv) (S) (III) (iii) (R) (d) (II) (ii) (Q)Which of the following option is the only incorrect combination?(III) (i) (R) (b) (I) (iii) (P)(II) (iii) (P) (d) (II) (iv) (Q)Which of the following options is the only CORRECT combination?(I) (ii) (R) (b) (II) (iii) (S)(III) (iv) (P) (d) (IV) (i) (S)

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