Consider the following statements in respect of the function f(x)=x in the interval (-1,1) : I. The function attains maximum value. II. The function attains minimum value. Which of the statements given above is/are correct ?

Step-by-step solution

Given the function f(x) = x defined on the open interval (-1, 1) . For any x (-1, 1) , we have -1 Since the interval is open, x can be arbitrarily close to 1 but never equals 1 . Thus, f(x) does not attain a maximum value in the given interval. Similarly, x can be arbitrarily close to -1 but never equals -1 . Thus, f(x) does not attain a minimum value in the given interval. Therefore, neither statement I nor statement II is correct. Answer: Neither I nor II