Suppose fProve that[a, b]→ R is continuous on[a, b] and differentiable on (a, b), and let ce (a, b).lim f'(x) extsts, then f' is continue at c.I-C

f:a, b→ℝ is continuous on a, b and differentiable on a, b.Also, c∈a, b.

Answered: Suppose f [a, b] → R is continuous…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose f [a, b] → R is continuous on[a, b] and differentiable on (a, b), and let c € (a, b). Prove that lim f'(r) extsts, then f' is continue at c. 2-4c