Réponses

2014-01-26T10:44:59+01:00
Bonjour

1) f(t) = 0.25 t^3 - 1.5 t^2 + 15\\\\f'(t)=0,75t^2-3t\\\\f'(t)=0,5\times1,5t^2-2\times1,5t\\\\f'(t)=1,5t\times0,5t-2\times1,5t\\\\f'(t)=1,5t(0,5t-2)

2) Signe de f'(t) et variations de f

racine : 0,5t - 2 = 0 ==> 0,5t = 2 ==> t = 2/0,5 ==> t = 4

\begin{array}{|c|ccccc||}t&0&&4&&10\\ 1,5&&+&+&+&\\ 0,5t-2&&-&0&+&\\ f'(t)&&-&0&+& \\ f(t)&15&\searrow&7&\nearrow&115 \\\end{array}