The minimum value of the expression 3 x + 2 y ( ∀ x , y > 0 ), where x y 2 = 10, occurs when the value of y is equal to

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The minimum value of the expression

3 x + 2 y (\forall x, y > 0),

where

x y^{2} = 10,

occurs when the value of

y

is equal to

MathematicsApplication of DerivativesJEE Main

Options:

A $\sqrt{10}$
B $\sqrt[3]{10}$
C $\sqrt[3]{30}$
D $\frac{1}{\sqrt{30}}$

Solution:

2943 Upvotes Verified Answer

The correct answer is:

\sqrt[3]{30}

3 x + 2 y = 3 (\frac{10}{y^{2}}) + 2 y = f (y) = \frac{30}{y^{2}} + y + y

Minimum value occurs when

y = {(30)}^{\frac{1}{3}}

(u s i n g A M \geq G M)

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