Which of the following statements is false for a function f that can be differentiated at least twice? a) If f ′ (c) = 0 and the sign of the derivative function f ′ (x) at point c changes from "+" to "-", point c is definitely the local maximum point of the function. b) If f ′ (c) = f ′ ′ (c) = 0, point (c, f (c)) is definitely the inflection point of the function graph. c) If f ′ (c) = 0 and f ′ ′ (c)> 0, point c is definitely the local minimum point of the function. d) If f ′ (c) = 0 and f ′ ′ (c) <0, point c is definitely the local maximum
Which of the following statements is false for a function f that can be differentiated at least twice?
a) If f ′ (c) = 0 and the sign of the derivative function f ′ (x) at point c changes from "+" to "-", point c is definitely the
b) If f ′ (c) = f ′ ′ (c) = 0, point (c, f (c)) is definitely the inflection point of the function graph.
c) If f ′ (c) = 0 and f ′ ′ (c)> 0, point c is definitely the
d) If f ′ (c) = 0 and f ′ ′ (c) <0, point c is definitely the local maximum point of the function.
e) If f ′ (c) = 0 and the sign of the derivative function f ′ (x) at point c changes from "-" to "+", point c is definitely the local minimum point of the function.
f) none
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