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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?

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

1 Answer 1

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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.

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  • $\begingroup$ 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. $\endgroup$ Sep 15, 2022 at 11:17

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