Let $a\in X$ be a local max point for the function $f:X\to\Bbb{R}$. If $f$ has a right derivative at $a$, then $f'_+(a)\leq0$.

Question

Let $a\in X$ be a local max point for the function $f:X\to\Bbb{R}$. If $f$ has a right derivative at $a$, then $f'_+(a)\leq0$.

Dem: If $f'_+\gt0$, then exists some $\delta$ such that $a

This is a review from a question i found. I understand the geometric concepts behind, but i didn't get the algebric concepts, i.e. why he used $a

Answer 1

Let $a\in X\subset\Bbb{R}$ be a local max point for the function $f:X\to\Bbb{R}$. Then there exists some $\delta$ such that for $a