The function f(x) = |x+1| on the interval [-2,0] is
A
continuous and differentiable
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B
Continuous on the integers but not differentiable at all points
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C
neither continuous nor differentiable
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D
differentiable but not continuous
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Solution
The correct option is B Continuous on the integers but not differentiable at all points f(x) = |x+1|
= -(x+1) for x < -1
= (x+1) for x ≥ -1
Only concern is x = -1
Left limit = limx→−1−−(x+1)=0
Right limit = limx→−1+(x+1)=0
f(x) is continuous in the interval [-2,0]
LD = -1
Right Derivative = + 1
Hence f(x) is not differentable at x = -1
Alternative Solution :
It is clear from graph f(x) is continuous every where but not differentiate at x = -1 because there is sharp change in slope at x = -1.