The largest area of a rectangle which has one side on the x-axis and the two vertices on the curve y=e-x2 is

Question

The largest area of a rectangle which has one side on the x-axis and the two vertices on the curve y=e-x2 is (A) √2 e -1 / 2 (B) 2 e -1 / 2 (C) e-1 / 2 (D) none

Tardigrade Admin · Accepted Answer

Let A be area A=(2 x)(e-x2), x > 0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/7657790b9a6db9070790e018711b6e8a-.png" /> ( d A / dx )=-2( x +(1/√2))( x -(1/√2)) e - x 2 At x=(1/√2), A is maximum. Largest area is 2 (1/√2) e -1 / 2

Q. The largest area of a rectangle which has one side on the $x$ -axis and the two vertices on the curve $y = e^{- x^{2}}$ is

$2 e^{- 1/2}$

$2 e^{- 1/2}$

$e^{- 1/2}$

none

Let $A$ be area $A = (2 x) (e^{- x^{2}}), x > 0$

$\frac{d A}{d x} = - 2 (x + \frac{1}{2}) (x - \frac{1}{2}) e^{- x^{2}}$
At $x = \frac{1}{2}$ , A is maximum.
Largest area is $2 \frac{1}{2} e^{- 1/2}$

Q. The largest area of a rectangle which has one side on the x-axis and the two vertices on the curve y=e−x2 is

2​e−1/2

2e−1/2

e−1/2

none

Let A be area A=(2x)(e−x2),x>0 dxdA​=−2(x+2​1​)(x−2​1​)e−x2 At x=2​1​, A is maximum. Largest area is 22​1​e−1/2

Q. The largest area of a rectangle which has one side on the $x$ -axis and the two vertices on the curve $y = e^{- x^{2}}$ is

$2 e^{- 1/2}$

$2 e^{- 1/2}$

$e^{- 1/2}$

Let $A$ be area $A = (2 x) (e^{- x^{2}}), x > 0$

$\frac{d A}{d x} = - 2 (x + \frac{1}{2}) (x - \frac{1}{2}) e^{- x^{2}}$
At $x = \frac{1}{2}$ , A is maximum.
Largest area is $2 \frac{1}{2} e^{- 1/2}$