## Exam-Style Question on Differentiation## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 385. This question is similar to one that appeared on an IB AA Standard paper (specimen) for 2021. The use of a calculator is allowed.

The displacement, in millimetres, of a particle from an origin, O, at time t seconds, is given by \(s(t) = t^3 cos t + 5t sin t\) where \( 0 \le t \le 5 \) .

(a) Find the maximum distance of the particle from O.

(b) Find the acceleration of the particle at the instant it first changes direction.

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