velocity will be a maximum when dv/dt=0
we find an expression for v by differentiating s(t)
v = ds/dt = 256 t - 4t^3
then, dv/dt = 256 - 12 t^2
dv/dt is a max when dv/dt =0
256 - 12t^2 = 0 => t = +/- 4.62 s
in the interval in question, the max occurs at t=+4.62 s
let's do the second derivative test to ensure this extremum is a max:
d^2v/dt^2 = -24t
for t>0, the second derivative is <0 therefore this is a max
we find an expression for v by differentiating s(t)
v = ds/dt = 256 t - 4t^3
then, dv/dt = 256 - 12 t^2
dv/dt is a max when dv/dt =0
256 - 12t^2 = 0 => t = +/- 4.62 s
in the interval in question, the max occurs at t=+4.62 s
let's do the second derivative test to ensure this extremum is a max:
d^2v/dt^2 = -24t
for t>0, the second derivative is <0 therefore this is a max