If you set a function equal to zero and solve for x, then you are finding where the function crosses the x-axis.
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The antiderivative of a function which is equal to 0 everywhere is a function equal to 0 everywhere.
When the first derivative of the function is equal to zero and the second derivative is positive.
Take the derivative of the function and set it equal to zero. The solution(s) are your critical points.
The only trig functions i can think of with horizontal assymptotes are the inverse trig functions. and they go assymptotic for everytime the non-inverse function is equal to zero.
The identity function.