Let $f$ be a real-valued differentiable function defined on the real line $\mathbb { R }$ such that its derivative $f ^ { \prime }$ is zero at exactly two distinct real numbers $\alpha$ and $\beta$. Then, (A) $\alpha$ and $\beta$ are points of local maxima of the function $f$. (B) $\alpha$ and $\beta$ are points of local minima of the function $f$. (C) one must be a point of local maximum and the other must be a point of local minimum of $f$. (D) given data is insufficient to conclude about either of them being local extrema points.
Let $f$ be a real-valued differentiable function defined on the real line $\mathbb { R }$ such that its derivative $f ^ { \prime }$ is zero at exactly two distinct real numbers $\alpha$ and $\beta$. Then,\\
(A) $\alpha$ and $\beta$ are points of local maxima of the function $f$.\\
(B) $\alpha$ and $\beta$ are points of local minima of the function $f$.\\
(C) one must be a point of local maximum and the other must be a point of local minimum of $f$.\\
(D) given data is insufficient to conclude about either of them being local extrema points.