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Statement of a problem № m607

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Let be a continuous real-valued function on the unit circle {x € R2 : |x| =1} such that f (0, 1) = g(1, 0) = 0 and g(- x )= - g(x). Define f: R2->R by F (x) = {|x| . g (x/|x| x ≠0, 0 x = 0. (a) If x € R2 and h: R ->R is defined by h (t) = f (tx) show that h is differentiable. (b). show that f is not differentiable at (0, 0) unless g = 0.




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