The derivative of the given function at [tex]x=3[/tex] is required.
The value of the derivative f'(x) at x=3 does not exist.
The given equation is
[tex]f(x)=2+|x-3|[/tex]
The derivative of the given function for [tex]x>3[/tex] is
[tex]f'(x)=x-1[/tex]
The derivative of the given function for [tex]x<3[/tex] is
[tex]f'(x)=5-x[/tex]
At [tex]x=3[/tex] the function does not exist.
So, the derivative of the function at [tex]x=3[/tex] does not exist.
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