Please help

h(t)=-t²+12t+5​

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