Let $f: D \rightarrow R$, $D \subseteq R$, $c \in D$ and $r$ be a non-zero real number. Consider the following statements:
$Y$. $c$ is an extreme point of $f \Rightarrow c$ is an extreme point of $rf$
$M$. $c$ is an extreme point of $f \Rightarrow c$ is an extreme point of $r+f$
Which of the following is correct?

• A
  Only $Y$ is true
• B
  Only $M$ is true
• C
  Both $Y$ and $M$ are true
• D
  Neither $Y$ nor $M$ is true