# maximum and minimum

• Mar 7th 2009, 02:16 PM
math123456
maximum and minimum
The amount of current in an electrical system is given by the function
c(t)= -t^3 + t^2 + 21 t, where t is time in seconds and 0<t<5. Determine the times at which the current is maximal and minimal, and the amount of current in the system at these times.
• Mar 7th 2009, 02:34 PM
JeWiSh
Quote:

Originally Posted by math123456
The amount of current in an electrical system is given by the function
c(t)= -t^3 + t^2 + 21 t, where t is time in seconds and 0<t<5. Determine the times at which the current is maximal and minimal, and the amount of current in the system at these times.

$-t^3+t^2+21t$
$\frac{dy}{dx} = -3t^2+2t+21=0$
$3t^2-2t-21=0 = (t+3)(3t+7)$
$t=3$ or $t=\frac{-7}{3}$
If you differentiate $3t^2-2t-21$ again to get the maximum and minimum you get $6t-2$. So if you put in t=3, then 6t-2 is positive, therefore it is a minimum. If you put in t =-7/3 then 6t-2 is negative, so that is a maximum.

Oh right, I didn't see that it said 0<t<5. In that case the smallest possible value you can get in that range is t=0.