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 youranswer. If it is true, prove it directly. Hint: often times, the easiest way to prove something is false isby 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→0h²THEN f is twice differentiable at z = a.TrueFalseexists,(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 TrueO False

We have to check whether given statement is True or False.

Answered: (b) IF there exists a function m(z)…

(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

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.1: Limits

Problem 77E

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Question

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

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