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tmua.me Extreme Set C Paper 1 · Q16

Paper 1Geometry

For a real constant hh, consider the curves

C1:y=x33−x2,C2:y=(x−2)33−x−22+h.C_1:\quad y=\frac{x^3}{3}-\frac{x}{2}, \qquad C_2:\quad y=\frac{(x-2)^3}{3}-\frac{x-2}{2}+h.

For each value of hh for which the curves meet and their tangents are perpendicular at an intersection, the area enclosed by the two curves is calculated.

What is the sum of the squares of the distinct areas obtained?

A89\dfrac89
B2828
C5656
D10009\dfrac{1000}{9}
E112112
F224224

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