question_answer

For which value of x, the function \[f(x)={{x}^{2}}-2x\] is decreasing                                      [BIT Ranchi 1990]

A)            \[x>1\]

B)            \[x>2\]

C)            \[x<1\]

D)            \[x<2\]

Correct Answer: C

Solution :

           \[f(x)={{(x-1)}^{2}}-1\]. Hence decreasing in x < 1.            Aliter : \[f'(x)=2x-2=2(x-1)\]                    To be decreasing, \[2(x-1)<0\Rightarrow (x-1)<0\Rightarrow x<1\].