If f(t)=(t^2+2t+2)(7t^2+4), find f'(t), find f'(5)

Answer 1

f(t) = (t^2 +2t +2)(7t^2 +4)

= 7t^4 + 14t^3 + 18t^2 + 8t + 8

f'(t) = 28t^3 + 42t^2 + 36t + 8

f'(5) = 28(5^3) + 42(5^2) + 36(5) + 8

= 28(125) + 42(25) + 180 + 8

= 3500 + 1050 + 188

= 4550+ 188

= 4738