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

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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

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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 1
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 1 (21.04 KiB) Viewed 35 times
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. (30 21 T 1
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