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Answer: Yes. Consider the following example: $y=x(x+1)(x-1).$ This is a polynomial. Clearly it is differentiable everywhere. hence unique tangent exists at every point on the curve. Now at the point $(1/sqrt{3},-2/3sqrt{3})$ the tangent is horizontal and intersects the curve. Here $sqrt{r}$ denotes the square root of the positive real number $r$. Notice that $y$ is negative for $x<-1$ and positive for $x>1$. $y$ is positive between $-1 By: Prof. D. Bahuguna     Date: 2012-11-30

Answer: Yes. Consider the following example: $y=x(x+1)(x-1).$ This is a polynomial. Clearly it is differentiable everywhere. hence unique tangent exists at every point on the curve. Now at the point $(1/sqrt{3},-2/3sqrt{3})$ the tangent is horizontal and intersects the curve. Here $sqrt{r}$ denotes the square root of the positive real number $r$. Notice that $y$ is negative for $x<-1$ and positive for $x>1$. $y$ is positive between $-1 By: Prof. D. Bahuguna     Date: 2012-11-30