If at each point of the curve y = x³-ax²+x+1 the tangent is inclined at an acute angle with the positive direction of the x -axis then what is a or where it lies in between?

y'=3x²-2ax+1>0, find the two roots of 3x²-2ax+1=0,for positivity x should be lesser than both roots OR greater than both roots. x<a-√(a²-12) OR x>a+√(a²-12), it is clear that the roots are complex conjugate. a²<12

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