Question 977588
Find the derivative,
{{{dC/dt=((3t^2+2)12-(12t+4)(6t))/(3t^2+2)^2}}}
{{{dC/dt=(36t^2+24-72t^2-24t)/(3t^2+2)^2}}}
{{{dC/dt=(-36t^2-24t+24)/(3t^2+2)^2}}}
{{{dC/dt=(-12(3t^2+2t-2))/(3t^2+2)^2}}}
Set the derivative equal to zero.
{{{3t^2+2t-2=0}}}
{{{t^2+(2/3)t-2/3=0}}}
{{{t^2+(2/3)t+1/9=2/3+1/9}}}
{{{(t+1/3)^2=7/9}}}
{{{t+1/3=0 +- sqrt(7)/3}}}
{{{t=-1/3 +- sqrt(7)/3}}}
Only use the positive time value.
{{{t=-1/3 + sqrt(7)/3}}}