anonymous
  • anonymous
Find the area of the largest rectangle with a base on the positive x axis, its right side on the line x=9 and which is inscribed under the curve f(x) = root(x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
I don't get it... can anybody help please?
mattfeury
  • mattfeury
you have to integrate on root(x) from x=0 to x=9.
mattfeury
  • mattfeury
actually that doesn't give you a rectangle. hmmm....

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anonymous
  • anonymous
elaborate please
mattfeury
  • mattfeury
this is the graph. it is strange though because at x=0, y = 0
anonymous
  • anonymous
screen shot is nothing
anonymous
  • anonymous
hmm, i can't see anything
mattfeury
  • mattfeury
*hopefully*
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mattfeury
  • mattfeury
you have to find the largest rectangle possible. looking at the graph i would guess (4,2) but that's just a though....
anonymous
  • anonymous
apparently we have to do it through optimization - derivatives and all that fun stuff
anonymous
  • anonymous
This is one of those questions you ask an instructor whose got over 20 yrs cal experience.
mattfeury
  • mattfeury
find a function for the area of the square and optimize. the area of the square at a given x up until 9 = x*y = sqrt(x) * (9-x)
mattfeury
  • mattfeury
try deriving that and see if find an extrema
anonymous
  • anonymous
not really :) as long as you have the skill then it's no prob
anonymous
  • anonymous
it's one of those questions that are a challenge ^_^
anonymous
  • anonymous
loving the enthusiasm sstarica, but i'm getting mercilessly owned in cal a
anonymous
  • anonymous
LOL, nah, let it be the opposite. It's quite simple, believe me :)
anonymous
  • anonymous
logically, I'd say the following: since the lenght of the rectangle is = 9, and is under the sqrt(x) now, let's first draw sqrt of (x) and notice that when you take x = 9, you'llhave y = 3. Logically, the rectangle won't exceed this limit, so the width is equal = 3
anonymous
  • anonymous
length*
myininaya
  • myininaya
matt has ir right! good job
anonymous
  • anonymous
since it's inscribed under it
mattfeury
  • mattfeury
yes the maxima of that graph is 3!
anonymous
  • anonymous
:) no need for all this.
myininaya
  • myininaya
now we need to find A'
anonymous
  • anonymous
all you had to do is draw sqrt(x) and see the limit of the rectangle. ^_^
anonymous
  • anonymous
why A'? doesn't he want A?
anonymous
  • anonymous
A = 3 x 9 = 27 that if he asked for A right? ^_^
myininaya
  • myininaya
to maximize you find A'
mattfeury
  • mattfeury
so it's 3 * sqrt(3)
mattfeury
  • mattfeury
or no. 6 * sqrt(3)
anonymous
  • anonymous
oh right lol my bad
myininaya
  • myininaya
yes x=3 is right matt thats are only critcal number thats in the domain of A
anonymous
  • anonymous
wait wait, why is 9=xy? doesn't A=xy?
anonymous
  • anonymous
since he wants the largest area, then yes maximize, proceed matt and hope you understood what was going on Ire :)
myininaya
  • myininaya
i didnt see A=9 up there no
anonymous
  • anonymous
you want the largest area, so you have to maximize in this case, they didn't ask for the "area" alone, but largest one
mattfeury
  • mattfeury
right. to find where the area is a maximum, take a function for the area and find the maxima point. take that point to make your rectangle. since you go up to 9 the x width is (9-3) = 6. the height of the rectangle is sqrt(3)
anonymous
  • anonymous
could you remind me how to find the maxima point please?
anonymous
  • anonymous
which means "optimize" lol, alight matt will take it from here ^_^ good luck
mattfeury
  • mattfeury
take the derivative of the area function 'A'. find where the derivative = 0.
mattfeury
  • mattfeury
normally, you'd have to do the second derivative test to find out if it is a max/min too. but i know secrets.
anonymous
  • anonymous
hmm
anonymous
  • anonymous
1. A = (9-x) * sqrt(x)
myininaya
  • myininaya
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anonymous
  • anonymous
wow, thanks guys
mattfeury
  • mattfeury
very nice.
myininaya
  • myininaya
also i never use the second derivative test it is pointless you can use A' to see if it is increasing to decreasing at x=3 to find that it is a max
myininaya
  • myininaya
The first derivative rocks!
anonymous
  • anonymous
thanks for the help guys, really appreciated

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