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Higher Maths: Optimisation

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!

Optimisation.jpg50.8KB

Reply 1

Dado Prso

7

try to get the height in terms of x.

if you're still struggling:

Spoiler

Reply 2

CT_Scan

For part b, do you just differentiate?

Reply 3

FuturePilot

OP

2

Dado Prso

try to get the height in terms of x.

if you're still struggling:

Spoiler

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!

Reply 4

FuturePilot

OP

2

CT_Scan

For part b, do you just differentiate?

Yeah, then nature table.

Reply 5

CT_Scan

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:

Reply 6

spacepirate-James

18

Part b:

Differentiate

Nature Table

Equate to 0

Then Solve

Methinks :s-smilie:

Reply 7

Dado Prso

7

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.

Reply 8

FuturePilot

OP

2

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

Reply 9

Lulope

9

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?

Reply 10

TheUnbeliever

16

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)

Reply 11

Lulope

9

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! :smile:

I have a horrible feeling I integrated instead of differentiating :facepalm2:

Reply 12

AndrewBodie

-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
.

Reply 13