Mathematics

Problem

Let

y(x)

be a solution of

\dfrac{dy}{dx}=(y-2)(x+1)

that passes through the point

(-1,3)

. Which of the following statements about the point

(-1,3)

on the solution curve is true? a) It is an inflection point because

\frac{dy}{dx}=0

and the concavity changes sign there. b) It is a point of relative maximum because

\frac{dy}{dx}

changes from positive to negative and the curve is concave down there. c) It is a point of relative minimum because

\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

\frac{dy}{dx}=0

but

\frac{d^2y}{dx^2}\neq 0

at that point.