The function f(x) = xˣ is strictly increasing for:
The function f(x) = xˣ is strictly increasing for:
- A. x < 1/e
- B. x > e
- C. x > 1/e
- D. x < e
Answer: C) x > 1/e
Explanation: Let y = xˣ. Taking log, log y = x log x. Differentiating, (1/y)(dy/dx) = 1 + log x. So f'(x) = xˣ(1 + log x). f'(x) > 0 implies log x > -1, so x > 1/e.
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