Question

If f(x)=xˣ, then f(x) is increasing in interval

• A. [0,e]
• B. [0,(1)/(e)]
• C. [0,1]
• D. None of these

Hint:

For xˣ, monotonicity depends on the sign of ln x+1.

Answer 1

The Correct Option is D

f'(x)=xˣ(ln x+1) f'(x)>0 when: ln x+1>0 ⟹ x>e⁻1 None of the given intervals exactly represent (e⁻1,∞).