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.
Suppose F X Is Defned On A B And Continuous At C Where A C B A 20 Marks Prove That If F Is Differentia 1 (27.89 KiB) Viewed 29 times
2. Suppose f(1) 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(0) = 0 separately.) (b) (10 marks) Is the condition that f is continuous at c necessary in (a)? Justify your answer. =
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