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?
Consider the following for the two (02) items that follow : Let the function f(x)=x^{2}+9.
- A. I only
- B. II only
- C. Both I and II
- D. Neither I nor II ✓
Correct Answer: D. Neither I nor II
Explanation
For f(x) = x^2+9, the derivative is f'(x) = 2x. The function decreases for x \lt 0 and increases for x \gt 0, so it is not strictly increasing everywhere (I is false). At x=0, f''(0) = 2 \gt 0, which means x=0 is a point of local minimum, not a maximum (II is false).
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