Determine whether the following statements are true and give an explanation or counterexample. a. If f'(c) =

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Determine whether the following statements are true and give an explanation or counterexample.

a. If f'(c) = 0, then f has a local maximum or minimum at c.

b. If f'(c) = 0, then f has an inflection point at c.

c. F(x) = x2 + 10 and G(x) = x2 - 100 are antiderivatives of the same function.

d. Between two local minima of a function continuous on (-∞, ∞), there must be a local maximum.

e. The linear approximation to f(x) = sin x at x = 0 is L(x) = x.

f. Iflim f(x) = o and lim g(x) 00 thenlim (f(x) – g(x)) = 0.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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