Verified Solution • 2025–26 Session moderate

QJEEM24Ma5d66: JEE Main 2024 Mathematics - Class 12 JEEM24Ma5d66 Solution: The function , has

The function f(x)=2x+3(x)23,x∈Rf(x)=2 x+3(x)^{\frac{2}{3}}, x \in \mathbb{R} , has

Multiple Choice Options

  • A exactly one point of local minima and no point of local maxima
  • B exactly one point of local maxima and exactly one point of local minima
  • C exactly two points of local maxima and exactly one point of local minima
  • D exactly one point of local maxima and no point of local minima

Step-by-Step Verified Solution

amp;f(x)=2x+3(x)23amp;f′(x)=2+2x−13amp;=2(1+1x13)amp;=2(x13+1x13)\begin{aligned}& f(x)=2 x+3(x)^{\frac{2}{3}} \\& f^{\prime}(x)=2+2 x^{\frac{-1}{3}} \\& =2\left(1+\frac{1}{x^{\frac{1}{3}}}\right) \\& =2\left(\frac{x^{\frac{1}{3}}+1}{x^{\frac{1}{3}}}\right)\end{aligned}

JEE Main 2024 (Online) 29th January Evening Shift Mathematics - Application of Derivatives Question 24 English Explanation

So, maxima (M) at x = −- 1 & minima (m) at x = 0

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