QCEVault

Further applications of differentiation — Question 357

Original QCE Vault practice · 6 marks

Q357 · Practice questionTechnology-activeComplex unfamiliar6 marks

QUESTION 357 (6 marks)

A closed cylindrical container must hold 32π cm332\pi\ \mathrm{cm}^3. Its radius is rr cm and height is hh cm. Material for its two circular ends costs 33 cents per cm2\mathrm{cm}^2, while material for its curved side costs 11 cent per cm2\mathrm{cm}^2. Ignore seams and waste.
a)
Develop a cost function in terms of rr only.
[2 marks]
b)
Determine the dimensions that minimise the cost, to two decimal places. Justify that the minimum is global.
[4 marks]
Question linkSyllabus coverage

Related questions

  1. Q3 · Original practice · 1 mark
    The graph shown is the graph of f′(x)f'(x). At which value of xx does ff have a local maximum?
    Further applications of differentiation
  2. Q13 · Original practice · 1 mark
    The stationary points of f(x)=x3−3x2−9x+4f(x)=x^3-3x^2-9x+4 occur when x=x=
    Further applications of differentiation
  3. Q23 · Original practice · 1 mark
    For f(x)=xe−xf(x)=xe^{-x} on x>0x>0, the xx-coordinate of the maximum point is
    Further applications of differentiation
  4. Q28 · Original practice · 4 marks
    A rectangle is inscribed symmetrically under the parabola y=12−x2y=12-x^2 and above the xx-axis, as shown. The upper right corner is (x,12−x2)(x,12-x^2), where 0<x<120<x<\sqrt{12}. Determine the maximum possible area of the rectangle.
    Further applications of differentiation