Consider the following for the two (02) items that follow: Let the function f(x) = x^2 + 9 . Consider the following statements: I. f(x) is an increasing function. II. f(x) has local maximum at x = 0 . Which of the statements given above is/are correct?

Step-by-step solution

Given f(x) = x^2 + 9 . Differentiating with respect to x , we get f'(x) = 2x . For x For x > 0 , f'(x) > 0 , which means f(x) is strictly increasing in (0, ) . Since f(x) is not increasing on its entire domain, Statement I is incorrect. To find local extrema, we set f'(x) = 0 , which gives x = 0 . The second derivative is f''(x) = 2 . Since f''(0) = 2 > 0 , f(x) has a local minimum at x = 0 , not a local maximum. Thus, Statement II is also incorrect. Both statements are incorrect. Answer: Neither I nor II