Local Extrema

Quite a simple concept that’s overcomplicated in the course. Take an interval $I$. Take a point $c$ in it.

Local Max: If $f(c)$ is the highest point in that interval $I$. (I.E. $f(c)>=f(x)$, where $x$ is any other point in $I$)
Local Min: Opposite of local max obviously lol.

Fun!!! FERMAT'S THEOREM!!!!!

If you find the crest or trough of a function and it’s differentiable, the derivative is 0!!! Who would have thought it… Mathematically:

If $f$ has a local extremum and is differentiable at $c$, then $f^{\prime }(x)=0$

• Related:
• Finding Extrema
• Rolle’s Theorem