--> Révision interrogation écrite n°3 Exercice 1 Soit f(x)f(x) == 0,2x21,2x3,20,2x^2-1,2x-3,2.
  1. Montrer que f(x)=0,2(x8)(x+2)f(x)=0,2(x-8)(x+2).
  2. Calculer f(x)f'(x).
Correction

  1. 0,2(x8)(x+2)0,2(x-8)(x+2) == 0,2(x2+2x8x16)0,2(x^2+2x-8x-16)
    == 0,2(x26x16)0,2(x^2-6x-16)
    == 0,2x20,2×6x0,2×160,2x^2-0,2\times6x-0,2\times16
    == 0,2x21,2x3,20,2x^2-1,2x-3,2.
    == f(x)f(x).

  2. f(x)f'(x) == 0,2×2x1,200,2\times2x-1,2-0
    == 0,4x1,20,4x-1,2.
Exercice 2 Soit f(x)f(x) == 0,3x20,6x+10,5-0,3x^2-0,6x+10,5.
  1. Montrer que f(x)=0,3(5x)(x+7)f(x)=0,3(5-x)(x+7).
  2. Calculer f(x)f'(x).
Correction

  1. 0,3(5x)(x+7)0,3(5-x)(x+7) == 0,3(5x+35x27x)0,3(5x+35-x^2-7x)
    == 0,3(x22x+35)0,3(-x^2-2x+35)
    == 0,3x20,3×2x+0,3×35-0,3x^2-0,3\times2x+0,3\times35
    == 0,3x20,6x+10,5-0,3x^2-0,6x+10,5.
    == f(x)f(x).

  2. f(x)f'(x) == 0,3×2x0,6+0-0,3\times2x-0,6+0
    == 0,6x0,6-0,6x-0,6.