JEE Advance - Mathematics (1993 - No. 22)
If $$f\left( x \right) = \left\{ {\matrix{
{3{x^2} + 12x - 1,} & { - 1 \le x \le 2} \cr
{37 - x} & {2 < x \le 3} \cr
} } \right.$$ then:
$$f(x)$$ is increasing on $$\left[ { - 1,2} \right]$$
$$f(x)$$ is continues on $$\left[ { - 1,3} \right]$$
$$f'(2)$$ does not exist
$$f(x)$$ has the maximum value at $$x=2$$