Question 868034

{{{V(t)=12t-4t^2}}}
{{{V(t+dt)=12(t+dt)-4(t+dt)^2}}}
You have a mistake here,
{{{V(t+dt)=12(t+dt)-4(t^2+2tdt+dt^2)}}}
{{{V(t+dt)=12t+12dt-4t^2-8tdt-4dt^2}}}
{{{V(t+dt)-V(t)=12dt-8tdt-4dt^2}}}
{{{(V(t+dt)-V(t))/dt=12-8t-4dt}}}
{{{dV/dt=lim(t->0,(V(t+dt)-V(t))/dt)=12-8t}}}