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The distance s metres from a fixed point O, covered by a particle after t seconds is given by the equation `s= t^3 -6t^2 + 9t +5`.
a).Calculate the gradient of the curve at t=0.5 seconds.
b).Determine the values of s at the maximum and the minimum turning points of curves.
c).Sketch the curve of `s= t^3 -6t^2 +9t+5`.