QCEVault

Further applications of differentiation — Question 23

Original QCE Vault practice · 1 mark

Q23 · Practice questionTechnology-freeComplex familiar1 mark

QUESTION 23

For f(x)=xe−xf(x)=xe^{-x} on x>0x>0, the xx-coordinate of the maximum point is
(A)
e−1e^{-1}
(B)
12\frac12
(C)
ee
(D)
11
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. 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
  4. Q38 · Original practice · 5 marks
    A 30 cm by 20 cm rectangular sheet has squares of side xx cm cut from each corner. The sides are folded up to form an open box. Determine the value of xx that maximises the volume and state the maximum volume to the nearest cubic centimetre.
    Further applications of differentiation