The points on the curve f x = x 1 - x 2 , where the tangent to it has slope equal to unity, are x 1 , y 1 , x 2 , y 2 and x 3 , y 3 . Then, x 1 + x 2 + x 3 is equal to

Question

The points on the curve f x = x 1 - x 2 , where the tangent to it has slope equal to unity, are x 1 , y 1 , x 2 , y 2 and x 3 , y 3 . Then, x 1 + x 2 + x 3 is equal to, 0, 3 2, 3 4, 3

MARKS App · Accepted Answer

f ′ x = 1 − x 2 1 − x − 2 x 1 − x 2 2 ⇒ 1 + x 2 = 1 + x 4 - 2 x 2 ⇒ x 4 - 3 x 2 = 0 ⇒ x = 0 , ± 3 ⇒ x 1 + x 2 + x 3 = 0

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