Find r'(t), r(t0), and r'(t0) for the given value of t0

Question

r'(t) = ____

r(t0) =____

r'(t0) =____

Answer 1

Since we have the vector r(t)=(t,t^2,5/4) we obtain the formulas r'(t)=(1,2t,0) and r''(t)=(0,2,0). So

r(2)=(2,4,5/4)

r'(2)=(1,4,0) and

r''(2)=(0,2,0).