What is the slope of functions at the edge case of $x=1$?

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SUMMARY

The discussion focuses on determining the slope of functions at the edge case of $x=1$. For the function $f(x)=x^2-1$, the slope at $x=1$ is calculated using the derivative, yielding a slope of 2, and the graph includes the point $(1,0)$. In contrast, for the linear function $f(x)=2x+1$, the slope at $x=1$ is 2, but the graph does not include the point $(1,0)$. These examples illustrate how to analyze slopes and points of intersection for different types of functions.

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Sithira
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How can you solve something like this ?

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Sithira said:
How can you solve something like this ?

Hi Sithira! Welcome to MHB! ;)

We have 2 edge cases here around the point(s) where $x=1$.

Suppose we had $f(x)=x^2-1$.
What would the slope be at $x=1$?
Does its graph include the point $(1,0)$?

As for the second edge case, suppose we had $f(x)=2x+1$.
What would the slope be at $x=1$?
Does its graph include the point $(1,0)$?
 

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