The minimum value of y=x(ℓ ln x)2 is-

Question

The minimum value of y=x(ℓ ln x)2 is- (A) 0 (B) 1 (C) 2 (D) None of these

Tardigrade Admin · Accepted Answer

y=x(ℓ n x)2 y prime=x ⋅ 2 ℓ n x ⋅ (1/x)+(ℓ n x)2 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/9e4c5c7161dcda6d0128de59c2c41feb-.png" /> y is min at x=1 ∴ y min =0

Q. The minimum value of $y = x (ℓ ln x)^{2}$ is-

0

1

2

None of these

$y = x (ℓ n x)^{2}$
$y^{'} = x \cdot 2 ℓ n x \cdot \frac{1}{x} + (ℓ n x)^{2}$

$y$ is $min$ at $x = 1$
$∴ y_{m i n} = 0$

Q. The minimum value of y=x(ℓlnx)2 is-

0

1

2

None of these

y=x(ℓnx)2 y′=x⋅2ℓnx⋅x1​+(ℓnx)2 y is min at x=1 ∴ymin​=0

Q. The minimum value of $y = x (ℓ ln x)^{2}$ is-

$y = x (ℓ n x)^{2}$
$y^{'} = x \cdot 2 ℓ n x \cdot \frac{1}{x} + (ℓ n x)^{2}$

$y$ is $min$ at $x = 1$
$∴ y_{m i n} = 0$