Verified Solution • 2025–26 Session moderate

QJEEM24Ma6763: JEE Main 2024 Mathematics - Class 12 JEEM24Ma6763 Solution: The interval in which the function , is strictly increasing is

The interval in which the function f(x)=x^x, x>0 , is strictly increasing is

Multiple Choice Options

  • A (0,∞)(0, \infty)
  • B (0,1e]\left(0, \frac{1}{e}\right]
  • C [1e2,1)\left[\frac{1}{e^2}, 1\right)
  • D [1e,∞)\left[\frac{1}{e}, \infty\right)

Step-by-Step Verified Solution

amp;f(x)=xxamp;f(x)=xx(log⁡x+1)amp;f(x)≥0amp;⇒1+log⁡x≥0amp;⇒log⁡x≥−1amp;⇒x≥e−1amp;∴x∈[1e′,∞)\begin{aligned}& f(x)=x^x \\& f(x)=x^x(\log x+1) \\& f(x) \geq 0 \\& \Rightarrow 1+\log x \geq 0 \\& \Rightarrow \log x \geq-1 \\& \Rightarrow x \geq e^{-1} \\& \therefore x \in\left[\frac{1}{e^{\prime}}, \infty\right)\end{aligned}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring