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If at each point of the curve y = x 3 -ax 2 +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?

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?

Grade:12

1 Answers

Chetan Mandayam Nayakar
312 Points
9 years ago

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

if you have any doubt, you can contact me at mn_chetan@yahoo.com

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