Question

Problem attached inside!!

Please explain? I don't get how to start this one at all:(

x=_________

**round to three decimal places if necessary***

thank you!!! @Luigi0210 :)

Answer 1

problem!

Answer 2

The area of the rectangle is length times width.

The length is x, the height is f(x).

So:

Area = x*f(x)

Plug in f(x)

Differentiate it, set equal to zero, solve for x.

Answer 3

so \[x * \frac{ x^2 }{ 3 } - 50x +1000\] ?

Answer 4

so you get \[\frac{ x^3 }{ 3 }-50x^2+1000x\] ?

Answer 5

@agent0smith and set it equal to 0 ? and solve for x?

Answer 6

Differentiate it, set equal to zero, solve for x.

Answer 7

not sure what the first term would differentiate to :/

but then it would be like this?

_______ - 100x + 1000 = 0
??

Answer 8

oh so

x^2 - 100x +1000 = 0 @agent0smith ?

Answer 9

Yes, then solve for x, there'll be two solutions, just make sure the one you get is a maximum. Easiest way is to graph the Area equation to check it's a max not min, and check it's in the domain 0<x<16.

Answer 10

x= 10 ( 5 + √15) ?

is that the max??

Answer 11

Idk, too tired to check, but a calculator or wolfram alpha can check for you.

Answer 12

Yours looks much bigger than 16, though...

Answer 13

Since 10*5 is 50

Answer 14

haha okay :P cool, thank you!!!

Answer 15

I think in this problem you select the negative square root
x= 10 ( 5 - √15)

Answer 16

because they put a restriction on x: 0 ≤ x ≤ 16

Answer 17

ahh okay... Thanks @phi :)