# Although there are many kinda like me, it all started with me

At the bottom I'm never happy or unhappy.
To the left of the bottom I'm always happy.
To the right of the bottom I'm always happy.

At the bottom my ' is never happy or unhappy.
To the left of the bottom my ' is always unhappy.
To the right of the bottom my ' is always happy.

Overall, at least I look happy.

Who Am I?

• Your what? Apostrophe (or something shaped like one)? Sep 14, 2022 at 19:37
• @dan04 It's part of the riddle. You have to figure out what that means. Sep 14, 2022 at 19:42

I think the answer might be

The function $$f(x) = x^2$$, or something similar

At the bottom I'm never happy or unhappy.

The bottom here refers to $$x=0$$ where the graph takes its minimum. At this point $$f(x)=0$$ which is neither positive nor negative (synonymous with happy/unhappy)

To the left of the bottom I'm always happy.

For $$x<0$$, $$f(x)$$ is always positive.

To the right of the bottom I'm always happy.

For $$x>0$$, $$f(x)$$ is always positive.

At the bottom my ' is never happy or unhappy.

' here refers to the first derivative which in this case is the function $$g(x) = 2x$$. I take the bottom here to still refer to the bottom of $$f(x)$$ and at $$x=0$$, $$g(x) = 0$$ which is neither positive nor negative.

To the left of the bottom my ' is always unhappy.

For $$x<0$$, $$g(x)$$ is always negative

To the right of the bottom my ' is always happy.

For $$x>0$$, $$g(x)$$ is always positive

Overall, at least I look happy.

The graph of $$f(x) = x^2$$ looks like a big smile.

• Great job! This is exactly the answer I had in mind. Although other rot13(tencuf) can fit, I tried to rule them out with the help of the title. Sep 15, 2022 at 11:17