Réponses

2013-03-27T14:43:20+01:00

Bonjour,

 

1)

Pour f(x) = 2x+1,5 :

\frac{f(2)-f(1)}{2-1} = \frac{5{,}5 - 3{,}5}{1} = 2\\ \frac{f(3)-f(1)}{3-1} = \frac{7{,}5-3{,}5}{2} = \frac{4}{2} = 2\\ \frac{f(1)-f(-2)}{1-(-2)} = \frac{3{,}5-(-2{,}5)}{3} = \frac 63 = 2\\ \frac{f(-2)-f(-3)}{-2-(-3)} = \frac{-2{,}5-(-4{,}5)}{1} = 2

 

Pour f(x) = -5x+4 :

\frac{f(2)-f(1)}{2-1} = \frac{-6 - (-1)}{1} = -5\\ \frac{f(3)-f(1)}{3-1} = \frac{-11-(-1)}{2} = \frac{-10}{2} = -5\\ \frac{f(1)-f(-2)}{1-(-2)} = \frac{-1-14}{3} = -5\\ \frac{f(-2)-f(-3)}{-2-(-3)} = \frac{14-19}{1} = -5

 

2)

1)f(x_2)-f(x_1) = (ax_2 +b)-(ax_1 +b)= ax_2-ax_1

2)f(x_2)-f(x_1) = a(x_2-x_1)\\ \frac{f(x_2)-f(x_1)}{x_2-x_1} = \frac{a(x_2-x_1)}{x_2-x_1} = a