Consider the function $$f(x) = - 2{x^3} - 9{x^2} - 12x + 1$$

The function f(x) is a decreasing function in the interval

Which one of the following statements is correct in respect of the function f(x) = x³ sin x?

Let $$f(x) = \left\{ {\matrix{ {3{x^2} + 12x - 1,} & { - 1 \le x \le 2} \cr {37 - x,} & {2 < x \le 3} \cr } } \right.$$

Which of the following statements is/are correct?

I. f(x) is increasing in the interval {$$-$$1, 2}.

II. f(x) is decreasing in the interval {2, 3}.

Select the correct answer using the code given below.

Let $$f(x) = \left\{ {\matrix{ {3{x^2} + 12x - 1,} & { - 1 \le x \le 2} \cr {37 - x,} & {2 < x \le 3} \cr } } \right.$$

Which of the following statements are correct?

I. f(x) is continuous at x = 2.

II. f(x) attains greatest value at x = 2.

III. f(x) is differentiable at x = 2.

Select the correct answer using the code given below.