For a positive real number $\alpha$, let $S_\alpha$ denote the set of points $(x, y)$ satisfying $$|x|^\alpha + |y|^\alpha = 1$$ A positive number $\alpha$ is said to be good if the points in $S_\alpha$ that are closest to the origin lie only on the coordinate axes. Then (A) all $\alpha$ in $(0,1)$ are good and others are not good. (B) all $\alpha$ in $(1,2)$ are good and others are not good. (C) all $\alpha > 2$ are good and others are not good. (D) all $\alpha > 1$ are good and others are not good.
For a positive real number $\alpha$, let $S_\alpha$ denote the set of points $(x, y)$ satisfying
$$|x|^\alpha + |y|^\alpha = 1$$
A positive number $\alpha$ is said to be good if the points in $S_\alpha$ that are closest to the origin lie only on the coordinate axes. Then\\
(A) all $\alpha$ in $(0,1)$ are good and others are not good.\\
(B) all $\alpha$ in $(1,2)$ are good and others are not good.\\
(C) all $\alpha > 2$ are good and others are not good.\\
(D) all $\alpha > 1$ are good and others are not good.