Statement - 1: The points on the curve y 2 = x + sin x at which the tangent is parallel to x-axis lie on a straight line. Statement - 2: If tangent is parallel to x-axis, then d x d y = 0 or d y d x

Question

Statement - 1: The points on the curve y 2 = x + sin x at which the tangent is parallel to x-axis lie on a straight line. Statement - 2: If tangent is parallel to x-axis, then d x d y ​ = 0 or d y d x ​ is undefined.

TestHub · Accepted Answer

∵ y 2 = x + sin x … ( i ) ∴ 2 y d x d y ​ = 1 + cos x = 0 ( ∵ d x d y ​ = 0 ) ∴ cos x = − 1 , then sin x = 0 From Eq. (i), y 2 = x (parabola), not a straight line. So Statement-1 is false and Statement-2 is true.

Mathematics - Application of Derivative Question with Solution | TestHub

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