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Solution


Q.

Let f:R→R be a function defined by f(x)=||x+2|–2|x||. If m is the number of points of local minima and n is the number of points of local maxima of f, then m + n is          [2025]
1 3  
2 4  
3 5  
4 2  

Ans.

(1)

We have, f(x)=||x+2|–2|x||

⇒ f(x)={(–x+2),x<–2(–3x–2),–2≤x<–23(3x+2),–23≤x<0(–x+2),0≤x<2(x–2),x>2

Critical points are x=–2,–23,0,2

Number of local maxima = 1 = n

Number of local minima = 2 = m

∴   m + n = 2 + 1 = 3.