Let be a solution of that passes through the point

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let y(x)y(x) be a solution of dydx=(y−2)(x+1)\dfrac{dy}{dx}=(y-2)(x+1) that passes through the point (−1,3)(-1,3). Which of the following statements about the point (−1,3)(-1,3) on the solution curve is true? (a) It is an inflection point because dydx=0\frac{dy}{dx}=0 and the concavity changes sign there. (b) It is a point of relative maximum because dydx\frac{dy}{dx} changes from positive to negative and the curve is concave down there. (c) It is a point of relative minimum because dydx\frac{dy}{dx} changes from negative to positive and the curve is concave up there. (d) It is neither an extremum nor an inflection point because dydx=0\frac{dy}{dx}=0 but d2ydx2≠0\frac{d^2y}{dx^2}\neq 0 at that point.

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