The sum of the coordinates of the point on the graph of f ( x ) = x 3 + 4 x the tangent at which is parallel to the chord joining the points (-2, -16) and ( 1 , 5 ) is

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Slope of chord = 1 − ( − 2 ) 5 − ( − 16 ) ​ = 3 21 ​ = 7 ; f ′ ( x ) = 3 x 2 + 4 By L.M.V.T ∃ c ∈ ( − 2 , 1 ) such that f ′ ( c ) = 7 : 3 c 2 + 4 = 7 ⇒ c = ± 1 ; ∴ c = − 1 Point = ( c , f ( c )) = ( − 1 , − 5 ) ; sum = − 6

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