The function f x = 2 x + 3 x 2 3 , x ∈ R , has

Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaEasy2 minPYQ_2024

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The function $f (x) = 2 x + 3 x^{\frac{2}{3}}, x \in R$ , has

Answer:

Solution:

Given: $f (x) = 2 x + 3 (x)^{\frac{2}{3}}$

$\Rightarrow f^{'} (x) = 2 + 2 x^{\frac{- 1}{3}}$

$\Rightarrow f^{'} (x) = 2 (1 + \frac{1}{x^{\frac{1}{3}}})$

$\Rightarrow f^{'} (x) = 2 (\frac{x^{\frac{1}{3}} + 1}{x^{\frac{1}{3}}})$

The function changes from positive to negative at $x = 1$ and from negative to positive at $x = 0$

So, the point of local maxima $(M)$ is at $x = - 1$ and the point of local minima $(m)$ at $x = 0$

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima

⏱ 2mℹ️ Source: PYQ_2024

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