JEE MAIN - Mathematics (2005 - No. 3)
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 |
|---|---|
| (- $$\infty $$, $$\infty $$) | x3 - 3x2 + 3x + 3 |
| Interval | Function |
|---|---|
| [2, $$\infty $$) | 2x3 - 3x2 - 12x + 6 |
| Interval | Function |
|---|---|
| $$\left( { - \infty ,{1 \over 3}} \right]$$ | 3x2 - 2x + 1 |
| Interval | Function |
|---|---|
| ($$ - \infty $$, - 4 ) | x3 + 6x2 + 6 |
Explanation
Clearly function $$f\left( x \right) = 3{x^2} - 2x + 1$$ is increasing
when $$f'\left( x \right) = 6x - 2 \ge 0 \Rightarrow \,\,\,\,\,x \in \left[ {1/3,\left. \infty \right)} \right.$$
$$\therefore$$ $$f(x)$$ is incorrectly matched with $$\left( { - \infty ,{1 \over 3}} \right)$$
when $$f'\left( x \right) = 6x - 2 \ge 0 \Rightarrow \,\,\,\,\,x \in \left[ {1/3,\left. \infty \right)} \right.$$
$$\therefore$$ $$f(x)$$ is incorrectly matched with $$\left( { - \infty ,{1 \over 3}} \right)$$
Comments (0)
