Question

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

• A. 5
• B. 3
• C. 2
• D. 4

Hint:

To find the number of local maxima and minima, determine the critical points of the function by finding where the derivative is zero or undefined. Then analyze the behavior of the function around these critical points using the first or second derivative test. For absolute value functions, consider the points where the expressions inside the absolute value signs change sign.

Answer 1

The Correct Option is B

\( f(x) = ||x+2| - 2|x|| \) 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