amathguy
amathguy
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Answer #2 is not a good counterexample. That function doesn't have a derivative at x=0: f'(0)=lim{[f(0+h) -f(0)]/h} = lim f(h)/h = 0 if h<0 and =1 if h>0 so the limit is undefined. So f is not differentiable at x=0. The wikepdia site (way…
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Answer #2 is not a good counterexample. That function doesn't have a derivative at x=0: f'(0)=lim{[f(0+h) -f(0)]/h} = lim f(h)/h = 0 if h<0 and =1 if h>0 so the limit is undefined. So f is not differentiable at x=0. The wikepdia site (way…