Question
Which of the following statements is/are true?
I.If f '(c) = 0, then f has a local maximum or minimum at x = c.
II.If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].
III.The Mean Value Theorem can be applied to f(x) = 1/x^2 on the interval [-1, 1].
I only
II only
I and III only
I and II only
I.If f '(c) = 0, then f has a local maximum or minimum at x = c.
II.If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].
III.The Mean Value Theorem can be applied to f(x) = 1/x^2 on the interval [-1, 1].
I only
II only
I and III only
I and II only
Answers
bobpursley
iii cannot be true at x=0 The function is not continous, which is a requirement for the MVT.
So would that mean that it is only the first one?
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