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tmua.me Tau Paper 1 · Q9

Paper 1CalculusGeometryAlgebra

Call a line admissible if it intersects y=x3−3xy=x^3-3x at three distinct points and the two finite regions between the line and the curve have areas in the ratio 32:532:5.

For some real number hh, exactly three distinct admissible lines pass through (h,0)(h,0). Let SS be the sum of their gradients.

Which one of the following describes all the possible values of SS?

AS>454S>\dfrac{45}{4}
BS≥454S\ge\dfrac{45}{4}
CS>9S>9
DS>814S>\dfrac{81}{4}
ES≥9S\ge9

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