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Assuming the function is
For
to be differentiable, it necessarily has to be continuous. For this condition to be met, we need
For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have
Now we solve for
and 
:
For
For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have
Now we solve for
Given:
The table of values is
x y
-4 2
-3 5
-2 8
-1 11
To find:
The slope of the line that contains these points.
Solution:
From the given table consider any two point.
Let the line passes through the points (-4,2) and (-3,5). So, the equation of the line is
Using distributive property, we get
Therefore, the required equation of line is .