A system which is represented by the given equation below, is able to work effectively even when the time is 0.                       f(t) = 7t^3 − 0.31t^2 + Idt − cos t However, there will be a time where the system is put on resting mode for several seconds. (i) Find the derivative of f(t).

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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A system which is represented by the given equation below, is able to work effectively even when the time is 0.
                      f(t) = 7t^3 − 0.31t^2 + Idt − cos t
However, there will be a time where the system is put on resting mode for several seconds.
(i) Find the derivative of f(t).

(ii) By using Newton-Raphson Method, select the approximate resting time in between the interval [1 2] seconds with the absolute system function tolerance is less than 0.0005 or until 4th iteration. Choose t0 = 1 sec.

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