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September 15, 2014

September 15, 2014

Posted by **George** on Tuesday, October 21, 2008 at 5:30pm.

Find the maximum area of such a triangle. Round your answer to 4 decimal places.

Maximum Area =

At what x-value does it occur?

Any help on these two questions would be greatly appreciated.

- Calculus -
**Reiny**, Tuesday, October 21, 2008 at 6:07pmArea of triangle = 1/2(base)(height)

= 1/2(x)(x^7)(e^(-7x)

= 1/2(x^8)(e^(-7x)

Area' = 1/2[x^8(-7e^(-7x)) + 8x^7(e^(-7x))]

= 0 for a max/min of Area

(1/2)e^(-7x)x^7[-7x + 8] = 0

-7x + 8 = 0

x = 8/7 or x = 1.142857

so max area = .000488145

test: take a slighter larger and a slightly smaller value of x

if x = 1.14

area = .000488133

if x = 1.15

area = .00048807

so the largest area correct to 4 decimals is .0005 and it occurs when x = 8/7

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