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Exercise 7.9. Assume f:R → R. (a) Let t € (1,0). Prove that if |f(x) =...

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Exercise 7.9. Assume f:R → R. (a) Let t € (1,0). Prove that if |f(x) = alt for all x, then f is differentiable at 0. (b) Let

Exercise 7.9. Assume f:R → R. (a) Let t € (1,0). Prove that if |f(x) = alt for all x, then f is differentiable at 0. (b) Let t € (0,1). Prove that if f(x) = |x|* for all x, and f(0) = 0, then f is not differentiable at 0. (c) Give a pair of examples showing that if |f(x)= |x|for all I, then either conclusion is possible.

Answers

Solution: - Assume fill R, Recall that, fis fis said to he differentiable at a GR, if Im for for enists Then we write H7A f c-as -0. Now, see that 4 fiozo as t 1 f(x)/x mit tecoil th = Plus tot 21 1291-7 f (2) - flo) 2-O * > M fue 1211-t ie TITLE Slo

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