Wednesday

August 20, 2014

August 20, 2014

Posted by **Alex** on Monday, January 3, 2011 at 5:59pm.

- Calculus -
**Reiny**, Monday, January 3, 2011 at 6:10pmThe curve looks sort of bell-shaped.

Let the point of contact in quadrant I be (x,y)

then the base of the rectangle is 2x and its height is y

A = 2xy

= 2x(e^(-x^2))

d(A)/dx = (2x)(-2x)(e^(-x^2)) + 2(e^(-x^2))

= 0 for a max/min of A

skipping some steps

e^(-x^2)) ( -2x + 1) = 0

x = 1/2

then y = e^(-1/4) = 1/e^(1/4)

so the rectangle has a length of 2x or 1

and a height of 1/e^(1/4)

- Calculus -
**Alex**, Monday, January 3, 2011 at 6:41pmCan you show me the steps you skipped?

Thanks

- Calculus -
**Reiny**, Monday, January 3, 2011 at 7:37pmfrom

(2x)(-2x)(e^(-x^2)) + 2(e^(-x^2)) = 0

-2e^(-x^2) ( -2x^2 + 1) = 0

**ahhh, just noticed an error from earlier, (that's what I get by skipping steps)**

-2e^(-x^2) = 0 ----> no solution

or

-2x^2 + 1 = 0

x^2 = 1/2

x = 1/√2

then y = e^(-1/2) = 1/√e

so the rectangle has a length of 2x or 2/√2

and a height of 1/√e

**Related Questions**

Calculus - Find the dimensions of teh rectangle with the most area that will ...

Calculus - Hello, could someone please help me with this problem? I'm a little ...

Calculus - Find the dimensions of the rectangle of largest area that has its ...

calculus - The graph of f'(x) is shown for 0=< x =<10. The areas of the ...

Calculus - Find the maximum area of a rectangle that lies above the x axis and ...

Calculus - Sketch the graph and find the area of the region described below. f(x...

calculus - A rectangle with its base on the x-axis is to be inscribed under the ...

calculus - A rectangle with its base on the x-axis is to be inscribed under the ...

calculus showed work - find the area of the rgion bounded by the graphs of y=x^3...

Calculus - find the area of the region described below. f(x)= -e^((1/2)x) Find ...