Question

How do you find the local extremas for `g(x) = - |x+6|`?

Answer 1

Differentiability is a stronger condition than continuity

`{ ("Differentiability", =>, "Continuity"), ("Continuity", NOT =>, "Differentiability" ) :}`

You cannot use calculus as although the function is continuous everywhere, it is not differentiable everywhere, and specifically it is not differentiable at the extrema that we seek (which happens to be a maximum)

But we can plot the function `y=-|x+6|`

graph{-|x+6| [-10, 10, -5, 5]}

And observer that there is a maximum at `(-6,0)`