For each statement, indicate whether it is true or false If false, correct the statement or explain why it is false (a) If '(c) 0, then (c) is either a local minimum or a local maximum (b) If (c) is the absolute maximum of on an interval I, then '(c) 0 (c) If is differentiable and (c) is a local mi...

a This statement is false The condition c 0 is not sufficient to guarantee that c is eith ...

For each statement, indicate whether it is true or false. If false, correct the statement or explain

Question:

For each statement, indicate whether it is true or false. If false, correct the statement or explain why it is false.
(a) If ƒ'(c) = 0, then ƒ (c) is either a local minimum or a local maximum.
(b) If ƒ (c) is the absolute maximum of ƒ on an interval I, then ƒ'(c) = 0.
(c) If ƒ is differentiable and ƒ(c) is a local minimum of ƒ, then ƒ'(c) = 0.
(d) If there is one local minimum of ƒ on an interval I, then it is the absolute minimum on I.

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