- #1

silicon_hobo

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**[SOLVED] is there a way to isolate x?**

## Homework Statement

Where does the tangent of tanh x = 1?

## Homework Equations

[tex]\\f(x)=\tanh x[/tex]

[tex]f^\prime(x)=\\sech^2x=1-\tanh^2x[/tex]

## The Attempt at a Solution

[tex]\\f^\prime(x)=1-\tanh^2x\rightarrow1-\tanh^2x=1\rightarrow\sqrt{\tanh^2x}=\sqrt{0}\rightarrow \tanh x=0[/tex]

Since I have shown that the tangent = 1 when tanh x = 0, I thought it may be sufficient to simply add another line saying x = 0 since we know (based on the definition of tanh) that if tanh x = 0 then x = 0. However, I am wondering if there is a way to approach this to actually isolate x without using this assumption? Does that make sense? Thanks for reading.

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