JEE Mains · Maths · STD 12 - 6. Application of derivatives
The function \(f(x)=2 x+3(x)^{\frac{2}{3}}, x \in \mathbb{R}\), has
- A exactly one point of local minima and no point of local maxima
- B exactly one point of local maxima and no point of local minima
- C exactly one point of local maxima and exactly one point of local minima
- D exactly two points of local maxima and exactly one point of local minima
Answer & Solution
Correct Answer
(C) exactly one point of local maxima and exactly one point of local minima
Step-by-step Solution
Detailed explanation
\( f(x)=2 x+3(x)^{\frac{2}{3}} \) \( f^{\prime}(x)=2+2 x^{\frac{-1}{3}} \) \( =2\left(1+\frac{1}{x^{\frac{1}{3}}}\right) \) \( =2\left(\frac{x^{\frac{1}{3}}+1}{x^{\frac{1}{3}}}\right) \) \( +\frac{1}{+}-\mathrm{m}^{-1}\) So, \(\operatorname{maxima}(\mathrm{M})\) at…
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