i) Determine "a" values for which f is differentiable at 0 and determine the f'(o) values.
ii) Determine "a" values for which f' is continuous at 0.
iii) Determine "a" values for which f"(0) exists and determine its value(s).
i) Determine "a" values for which f is differentiable at 0 and determine the f'(o) values.
ii) Determine "a" values for which f' is continuous at 0.
iii) Determine "a" values for which f"(0) exists and determine its value(s).
Have you tried anything? Like writing down the formula for the derivative at 0:
$\displaystyle \lim_{h\to 0}\frac{h^a sin(1/h)- 0}{h}= \lim_{h\to 0}h^{a-1}sin(1/h)$
Does that give you any ideas.
(I assume that your "and (0, 0) is a point" means that (0, 0) is a point in the graph of y= f(x)- in other words, that f(0)= 0.)