FuturePilot
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#1
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#1
Hey,
I've been trying to get this optimisation question.
I've got the answer to (b), but cannot for the love of me get part (a) :p:

Could someone give me some hints as to how you get it? :p:

Thanks!
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Dado Prso
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#2
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#2
try to get the height in terms of x.

if you're still struggling:
Spoiler:
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inner surface area = 2 sides + 2 sides + bottom
12=2(2xh)+2(xh) + 2x^2

then V=lbh
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CT_Scan
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#3
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For part b, do you just differentiate?
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FuturePilot
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#4
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(Original post by Dado Prso)
try to get the height in terms of x.

if you're still struggling:
Spoiler:
Show
inner surface area = 2 sides + 2 sides + bottom
12=2(2xh)+2(xh) + 2x^2

then V=lbh
Hey,
I managed to get the surface area earlier... but just can't work out the next bit :p:
Still can't get it :o: How I hate the first bit of these questions!
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FuturePilot
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#5
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(Original post by CT_Scan)
For part b, do you just differentiate?
Yeah, then nature table.
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CT_Scan
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(Original post by FuturePilot)
Yeah, then nature table.

Yeah, thanks for reassuring me. I am sorry but I cannot help you with the first part, have you had your prelim yet? Mines is tomorrow. :eek:
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spacepirate-James
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#7
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Part b:

Differentiate

Nature Table

Equate to 0

Then Solve

Methinks
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Dado Prso
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(Original post by FuturePilot)
Hey,
I managed to get the surface area earlier... but just can't work out the next bit :p:
Still can't get it :o: How I hate the first bit of these questions!
rearrange the surface area equation to get (6-x^2)/3x=h

v=lbh
v=2x^2 x (6-x^2/3x)

v=2x^2/3x x (6-x^2)

v=2x/3 (6-x^2) as required.
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FuturePilot
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#9
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(Original post by CT_Scan)
Yeah, thanks for reassuring me. I am sorry but I cannot help you with the first part, have you had your prelim yet? Mines is tomorrow. :eek:
No bother. Oh, good luck! Mine's on Friday
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Lulope
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Could someone help me with this one?

f(x) = 4x^2 - 14x +24

It was in our prelim and we had to find the answer which minimizes the function.

I think I did it the right way but I don't know if I got the right answer?
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TheUnbeliever
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(Original post by Lulope)
Could someone help me with this one?

f(x) = 4x^2 - 14x +24

It was in our prelim and we had to find the answer which minimizes the function.

I think I did it the right way but I don't know if I got the right answer?
f'(x) = 8x - 14

f'(x) = 0 at sps,
8x = 14
x = 7 / 4

(this is clearly going to be the minimum, since there aren't any other sps!)

f(7 / 4) = 4(49/16) - 14(7/4) + 24 = 49 / 4 - 49 / 2 + 24 = 0.25(49 - 98 + 96) = 47 / 4

(\frac{7}{4}, \frac{47}{4}) is the minimum tp of f.

(The way you've worded it sounds like you only needed x = 7 / 4 as the answer, though)
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Lulope
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(Original post by TheUnbeliever)
f'(x) = 8x - 14

f'(x) = 0 at sps,
8x = 14
x = 7 / 4

(this is clearly going to be the minimum, since there aren't any other sps!)

f(7 / 4) = 4(49/16) - 14(7/4) + 24 = 49 / 4 - 49 / 2 + 24 = 0.25(49 - 98 + 96) = 47 / 4

(\frac{7}{4}, \frac{47}{4}) is the minimum tp of f.

(The way you've worded it sounds like you only needed x = 7 / 4 as the answer, though)
Thank you!

I have a horrible feeling I integrated instead of differentiating :facepalm2:
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AndrewBodie
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#13
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#13
-differentiate and make equal to zero for x.
-find the second derivative (so differentiate again)
-substitute in x to the second derivative and if your answer is negative, it gives a Maximum
.
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Medic DUX
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#14
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7 years later ... they have probs got their degree now hahah
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