WOLFRAM|DEMONSTRATIONS PROJECT

Differentiation Microscope

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x
0
-1
zoom
The differentiation microscope for f(x)
2
x
+x
This differentiation microscope lets you graphically explore if a function is differentiable at a given point
x
0
. If you "zoom in" at any point
x
0
and you see that in a very close neighborhood of
x
0
the function looks like a linear function, then the function
f(x)
is differentiable at
x
0
, otherwise not. Can you find points where

2
x
+x
is differentiable and points where otherwise it is not?