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?
D. Neither I nor II
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
Related: Mathematics — Application of Derivatives · All PYQ Banks