Find the derivative of the curve \(f(x)=0.75x^4-10x^3+49.5x^2-108x+11\) and factorise the derivative to the form \(3(x+a)(x+b)^2\), where \(a\) and \(b\) are integers.[5]
Hence find the \(x\)-coordinates of each of the stationary points of the curve \(f(x)=0.75x^4-10x^3+49.5x^2-108x+11\).[2]
Find the nature of each stationary point.[4]
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Answer:(a) \(3(x-4)(x-3)^2\). (b) \(x=3,4\). (c) Stationary inflection at 3; minimum at 4.