question_answer

A function is matched below against an interval, where it is supposed to be increasing. Which of the following pairs is incorrectly matched? Interval                Function     AIEEE  Solved  Paper-2005

A) \[(-\infty ,\,\,-4]\]           \[{{x}^{3}}+6{{x}^{2}}+6\]

B) \[\left( -\infty ,\frac{1}{3} \right]\]           \[3{{x}^{2}}-2x+1\]

C) \[[2,\,\infty )\]                  \[2{{x}^{3}}-3{{x}^{2}}-12{{x}^{4}}-6\]

D) \[(-\infty ,\infty )\]                          \[{{x}^{3}}-3{{x}^{2}}+3x+3\]

Correct Answer: B

Solution :

Let On differentiating w.r.t.we get Forto be increasing \[f'(x)>0\]   Let This is wrong. Hence, option (b) is correct.