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(b) IF there exists a function m(z) with domain R such that f(r)-f(a)= m(x)(x-a). THEN f(z) is differentiable at z = a. True False

(b) IF there exists a function m(z) with domain R such that f(r)-f(a)= m(x)(x-a). THEN f(z) is differentiable at z = a. True False

Advanced Engineering Mathematics
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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please answer part b of this question

Let a € R. Let f be a function defined on R. Is each of the following claims true or false? Prove your answer. If it is true, prove it directly. Hint: often times, the easiest way to prove something is false is by providing a counter example and proving that counter example satisfies the required conditions. (a) IF the limit lim f(a+h)-2f(a) + f(a-h) h→0 h² THEN f is twice differentiable at z = a. True False exists, (b) IF there exists a function m(z) with domain R such that f(x) - f(a) = m(x)(x − a), THEN f(x) is differentiable at x = a. O True O False
Transcribed Image Text:Let a € R. Let f be a function defined on R. Is each of the following claims true or false? Prove your answer. If it is true, prove it directly. Hint: often times, the easiest way to prove something is false is by providing a counter example and proving that counter example satisfies the required conditions. (a) IF the limit lim f(a+h)-2f(a) + f(a-h) h→0 h² THEN f is twice differentiable at z = a. True False exists, (b) IF there exists a function m(z) with domain R such that f(x) - f(a) = m(x)(x − a), THEN f(x) is differentiable at x = a. O True O False
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