Find the nature of the turning points of the graph given by the equation x^4 +(8/3)*x^3 -2x^2 -8x +177 (6 marks)
(1 mark) Differentiate equation in the question: 4x3+8x2-4x-8(1 mark) Equate this to zero: (x-1)(x+1)(x+2)=0(1 mark) Find turning points (roots of above equation): x=1,-1,-2(1 mark) Differentiate again: 12x2+16x-4(2 marks) Evaluate the twice differentiated equation at each turning point to determine their nature: x=1: minimum ; x=-1: maximum ; x=-2: minimum
