g(t)= at^2+bt+c; g(1)= 5; g'(1)= 3; g"(1)= -4. Find a,b,c. I don't even know where to start. I know how to take the derivative and the 2nd, 3rd, 4th etc. But what am I suppose to do here.
$\displaystyle g(t) = at^2+bt+c$
$\displaystyle g'(t) = 2at + b$
$\displaystyle g''(t) = 2a$
from the given info for the three function vales at $\displaystyle t = 1$ ...
$\displaystyle 5 = a+b+c$
$\displaystyle 3 = 2a + b$
$\displaystyle -4 = 2a$
solve the system ...