A curve y = f (x) passing through the point (1, 1 e ) satisfies the differential equation…
Mathematics · JEE Advanced · NTA Exams — Differential Equations
A curve y = f (x) passing through the point \(\left(1, \frac{1}{\sqrt{\mathrm{e}}}\right)\) satisfies the differential equation \(\frac{\mathrm{dy}}{\mathrm{dx}}\) + \(x e^{-\frac{x^{2}}{2}}\)= 0. Then which of the following does not hold good?
- f (x) is differentiable at x = 0.
- f (x) is symmetric w.r.t. the origin.
- f (x) is increasing for x < 0 and decreasing for x > 0.
- f (x) has two inflection points.
Answer
(B) f (x) is symmetric w.r.t. the origin.
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