2. Suppose f() is defned on (a,b) and continuous at c, where a

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2 Suppose F Is Defned On A B And Continuous At C Where A C B A 20 Marks Prove That If F Is Differentiable A 1 (26.17 KiB) Viewed 24 times

2. Suppose f() 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. 3. (20 marks) Let f : [a, b] → R be integrable. Prove there there exists a point ce [a, b] such that ) dt | dt. [100 ) = ° 5(e) dt - L"50 ) 56) dt for 1 € (a, b)) (Hint: Use F(x)=