Let $ f : \mathbb{R} \rightarrow \mathbb{R} $ be a function defined by $ f(x) = ||x+2| - 2|x|| $. If m is the number of points of local maxima of f and n is the number of points of local minima of f, then m + n is
Let $ f : \mathbb{R} \rightarrow \mathbb{R} $ be a function defined by $ f(x) = ||x+2| - 2|x|| $. If m is the number of points of local maxima of f and n is the number of points of local minima of f, then m + n is
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- 5
- 3
- 2
- 4
The Correct Option is B
Solution and Explanation
\( f(x) = ||x+2| - 2|x|| \) Critical points are \( 0, -2, -\frac{2}{3} \)
No. of maxima = 1 No. of minima = 2 m = 1, n = 2 m + n = 1 + 2 = 3
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