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Grade: 11
        
Let f : R → R be a function defined by
f(x) = Min {x + 1, |x| + 1}.
Then which of the following is true? 
Give reason.

 (1) f(x) ≥ 1 for all x ∈ R
(2) f(x) is not differentiable at x = 1 
(3) f(x) is differentiable everywhere
(4) f(x) is not differentiable at x = 0
11 months ago

Answers : (1)

Aditya Gupta
1673 Points
							
Due to |x| greater than equal to x for all x belonging to R, f(x)= x+1
So obviously it is differentiable everywhere on the real line
11 months ago
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