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tmua.me Extreme Set A Paper 1 · Q6

Paper 1GeometryAlgebra

The curve CC has equation

y=x+1x,x>0.y=x+\frac1x,\qquad x>0.

The tangent and the normal to CC at a point PP meet the yy-axis at AA and BB, respectively. The origin is OO, and OA=OBOA=OB.

What is the gradient of the tangent at PP?

A2−73\dfrac{2-\sqrt7}{3}
B7−23\dfrac{\sqrt7-2}{3}
C2+73\dfrac{2+\sqrt7}{3}
D3−174\dfrac{3-\sqrt{17}}{4}
E3−145\dfrac{3-\sqrt{14}}{5}
FNo such point P exists\text{No such point }P\text{ exists}

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