QCEVault

Further applications of differentiation — Question 115

Original QCE Vault practice · 6 marks

Q115 · Practice questionTechnology-freeComplex unfamiliar6 marks

QUESTION 115 (6 marks)

A rectangular poster must contain a printed area of 600 cm2600\text{ cm}^2. The side margins are each 22 cm wide and the top and bottom margins are each 33 cm wide. Determine the dimensions of the printed area that minimise the total area of the poster, and state the minimum total area.
Rectangular poster showing a printed rectangle with 2 cm side margins and 3 cm top and bottom margins.
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