f(t)=t^3-12t^2+36t

Question

(e) Find the total distance traveled during the first 7 s.

Answer 1

f(t) = t³ - 12t² + 36t

f'(t) = 3t² - 24t + 36 = 3(t² - 8t + 12) = 3(t - 6)(t - 2) = 0 when t = 2 or t = 6.

When 0 < t < 2, f'(t) > 0. So, the object is moving to the right.

When 2 < t < 6, f'(t) < 0. So, the object is moving to the left.

When 6 < t < 7, f'(t) > 0. So, the object is moving to the right.

Total distance = [f(2) - f(0)] + [f(2) - f(6)] + [f(7) - f(6)] Evaluate!