shairn
Your favorite anime is bad.
So I'm studying for my analysis final and pull up the final from last semester as a reference, and there's an interesting bonus question:
"Give an example of a non-void set D ⊂R and a differentiable function f: D -> R such that D is included in the set of accumulation points of D, the derivative of f is equal to 0 for all x element of D and f is not constant."
I've thought of a composite function so that f is constant on either side of a point x0 but of a different value on either side (for example, the "floor" function on the interval [1.5 , 2.5]) but then it's not differentiable at the point x0 and if I exclude x0 from the domain, D is no longer included in the set of accumulation points of D. Though I guess that wouldn't work either since the limit would be different on either side.
Hm...
"Give an example of a non-void set D ⊂R and a differentiable function f: D -> R such that D is included in the set of accumulation points of D, the derivative of f is equal to 0 for all x element of D and f is not constant."
I've thought of a composite function so that f is constant on either side of a point x0 but of a different value on either side (for example, the "floor" function on the interval [1.5 , 2.5]) but then it's not differentiable at the point x0 and if I exclude x0 from the domain, D is no longer included in the set of accumulation points of D. Though I guess that wouldn't work either since the limit would be different on either side.
Hm...