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Could someone explain to me how to do these two optimisation questions.

1)

An open toppped box has height h cm and square base of side xcm.

The box has capacity Vcm^3. The area of its external surface consisting of its horizontal base and four vertical faces is Acm^2

a) Find expressions for V and A in terms of x and h.

b) It is given that A = 3000

i) Show that V=750x - 1/4x^3

ii) Find the positive value of x for which DV/dx = 0 giving your answer in surd form.

2)

Small trays are to be made from rectangular pieces of card. Each piece of card is 8cm by 5cm and the tray is formed by removing squaress of side xcm from each corner and folding the remaining card along the dashed lines.

a) Explain why 0 < x < 2.5

b) Show that the volume Vcm^3, of a tray is given by

c) Find the value of x for which dV/dx = 0

d) Calculate the greatest possible volume of a tray

1)

An open toppped box has height h cm and square base of side xcm.

The box has capacity Vcm^3. The area of its external surface consisting of its horizontal base and four vertical faces is Acm^2

a) Find expressions for V and A in terms of x and h.

b) It is given that A = 3000

i) Show that V=750x - 1/4x^3

ii) Find the positive value of x for which DV/dx = 0 giving your answer in surd form.

2)

Small trays are to be made from rectangular pieces of card. Each piece of card is 8cm by 5cm and the tray is formed by removing squaress of side xcm from each corner and folding the remaining card along the dashed lines.

a) Explain why 0 < x < 2.5

b) Show that the volume Vcm^3, of a tray is given by

V = 4x^3 - 26x^2 + 40x

c) Find the value of x for which dV/dx = 0

d) Calculate the greatest possible volume of a tray

1)

a) You should be able to do these.

b)

(i) Substitute 3000 into the equation you found for A in part a) in order to find h in terms of x. Then substitute this expression for h into your equation for V. Rearrange to give the required result.

(ii) Differentiate V wrt x, set to zero, solve quadratic.

a) You should be able to do these.

b)

(i) Substitute 3000 into the equation you found for A in part a) in order to find h in terms of x. Then substitute this expression for h into your equation for V. Rearrange to give the required result.

(ii) Differentiate V wrt x, set to zero, solve quadratic.

mikesgt2

1)

a) You should be able to do these.

b)

(i) Substitute 3000 into the equation you found for A in part a) in order to find h in terms of x. Then substitute this expression for h into your equation for V. Rearrange to give the required result.

(ii) Differentiate V wrt x, set to zero, solve quadratic.

a) You should be able to do these.

b)

(i) Substitute 3000 into the equation you found for A in part a) in order to find h in terms of x. Then substitute this expression for h into your equation for V. Rearrange to give the required result.

(ii) Differentiate V wrt x, set to zero, solve quadratic.

Interesting...

For b): I get...

x^2 + 4hx = 3000

And I was wondering how to solve for x...

2 2776

Yes. Or more aptly, 2776 is the same person as me.

why did u change ur screen name ???

- Econ+Maths joint honours, or straight Econ?
- Prior knowledge of maths for a Finance undergrad
- What shape area/volume equations do you need to know for Edexcel A Level maths?
- Is my Uni Grade Calculated Correctly(University of Westminster)?
- tmua grade for imperial
- What is more advanced: a Level 4 Diploma or a Level 5 Award?
- Moving departments in job
- My tutor just gave me access to her Save My Exams acocunt. How should i use it?
- how competitive is trinity for maths
- Lse Economics and Economic history…help please
- How useful do you find examiner’s reports? What should students focus on in these?
- Unit 7: BTECH IT Mobile App Development PART B & C
- Wanting to do Masters at Oxbridge
- Do AS exams matter?
- Best techniques to revise?
- India qualification for UG Math / Math + Stat
- Making an academic comeback halfway through second year
- DSA needs assessment
- what is seo
- Med / PA help

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