Answer Happy

Suppose f(x) is defined on (a, b) and continuous at c, where a
< c < b.
(a) Prove that if |f| is differentiable at c, then f is
differentiable at c. (Hint: Consider the cases f(c) > 0, f(c)
< 0, and f(c) = 0 separately.)
(b) Is the condition that f is continuous at c necessary in (a)?
Justify your answer.
Suppose f(x) is defned on (a,b) and continuous at c, where a <c<b. (a) (20 marks) Prove that if |f is differentiable at c, then f is differentiable at c. (Hint: Consider the cases f(c) > 0, f(c) <0, and f(c) = 0 separately.) (b) (10 marks) Is the condition that f is continuous at c necessary in (a)? Justify your answer.