Answer to Question #264599 in Real Analysis for Nikhil

Question #264599

The function f defined by :

f(x) = -| x-3| , x ∈ R has a local maxima.

True or false with full explanation

Expert's answer

Is well known:

"\\forall\\ x\\in\\mathbb{R}\\ |x|\\geq0\\Rightarrow -|x|\\leq0"

But "f(3)=-|3-3|=0" so f has a local maximum at point "3" .

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