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# Differentiation Watch

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1. Consider the function

(i) Calculate f'(x) for and show that does not exist. Done
(ii) Show, by definition of the derivative that f is differentiable at x = 0 and the derivative of f there. Done I think
(iii) Use this to answer the question: If a function has derivative defined at all points, is that derivative necessarily continuous? Done but depends on part 2
For the second part it says from the definition of the derivative so we use to get:

if x = 0:

Can I now say that if h goes to 0, the undefined fraction doesn't matter as the answer is always 0 (due to being multiplied by 0)?

Part 3:
If my answer for part 2 is correct then no the derivative doesn't have to be continuous?
2. For that last line you have, cos(a) is always in the interval [-1,1], so it's perfectly safe to say that
3. (Original post by marcusmerehay)
For that last line you have, cos(a) is always in the interval [-1,1], so it's perfectly safe to say that
Woop. Cheers!

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Updated: December 1, 2010
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