Answer:
Step-by-step explanation:
nate form assuming t is real:
h(t) + (t - 12) t = 5
Alternate forms:
h(t) = 5 - (t - 12) t
h(t) + t^2 = 12 t + 5
Roots:
t = 6 - sqrt(41)
t = 6 + sqrt(41)
Properties as a real function:
Domain
R (all real numbers)
Range
{h element R : h<=41}
Derivative:
d/dt(-t^2 + 12 t + 5) = -2 (t - 6)
Indefinite integral assuming all variables are real:
integral(-t^2 + 12 t + 5) dt = -t^3/3 + 6 t^2 + 5 t + constant
Global maximum:
max{-t^2 + 12 t + 5} = 41 at t = 6
