Re: help with a basic differentiability and derivative function

disanalysis wrote: 
very basic problem...can anyone help me with the proof?

f(x) = x^2-3x+8 if x>1
f(x) = 2x^2+x+3 if x=<1

using epsilon-delta property can you prove that f(x) is differentiable
at all points except x=1
and that it is not differentiable at 1?

thanx

At x = 1 f(x) = 6 from both expressions.

for x > 1, df(x)/dx = 2x-3 -> -1 as x -> 1 from the first expression, and

For x <= 1, df(x)/dx = 4x+1 = 5 at x=1.

So the first derivative of f(x) is discontinuous at just above x = 1. But, at x = 1 it is differentiable from the second expression which holds up to and including x = 1.
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