Question $3$:

$(8$ Marks$)$

A$)$ The position of a particle is given by the equation $s(t)=t^3-6t,$ where $s$ in meters and $t$ in seconds.

i$)$ What is the velocity of the particle after $3$ seconds?

ii$)$ What is the acceleration of the particle after $3$ seconds?

B$)$ Find the equation of the tangent line of $y=x^3-2x$ at $x=1.$

C$)$ Use the definition of the derivative to find $f^{(3)}$ where $f(x)=2x^2.$