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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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{7/3}
2013-05-25 17:17:02

Thanks

bob bundy
2013-05-25 16:47:30

hi {7/3}

At points where the function is 'well-behaved', yes.  eg. For your example, everywhere except x = 2.

At this point, it may still be ok.  It is continuous there, so it passes that hurdle.  You then need to consider whether there is a left limit for the chord gradient and a right limit, and whether they are the same.

So, whilst f(x) = 2x, the gradient function is 2, for all x.

Whilst f(x) = x^2, the gradient function is 2x, so the right limit, as x tends to 2, is 4.

So there is not a consistency between the gradient as x approaches 2 from the left, and the gradient as x approaches 2 from the right.  So it is said that it is not differentiable at this point.

Bob

{7/3}
2013-05-25 13:40:40

Can piecewise functions be differentiated?for example f(x)=2x for x<2,4 for x=2,x^2 for x>2,can f be differentiated?

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