Let the function f(x) = x² + 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?

Question

Accepted Answer

Neither I nor II. f(x) = x² + 9. f'(x) = 2x, which is negative for x < 0 and positive for x > 0, so f is not increasing throughout. At x = 0, f''(0) = 2 > 0, so x = 0 is a local minimum, not maximum. Both statements are false.

Let the function f(x) = x² + 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?

Explanation

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