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. Ifthen

Transcribed Image Text:

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