    Question

# If f(x)=⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩x2+2,x<0−2e−x,0≤x<2,−2e2(x−3),x≥2 then

A
|f(x)| is discontinuous at 0 points
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B
|f(x)| is discontinuous at 2 points
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C
|f(x)| is not differentiable at 2 points
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D
|f(x)| is not differentiable at 3 points
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Solution

## The correct option is C |f(x)| is not differentiable at 2 pointsGraph of f(x) Graph of |f(x)| The graph is discontinuous at 0 points Before x=0 the function is differentiable at all points because our function is a quadratic function. At x=2 and x=0, the function changes definition. So we need to check differentiability. At x=3, a linear function changes direction (sharp turn). So the function is not differentiable. At x=0 L.H.D. =0 R.H.D =−2e−x∣∣x=0=−2 So, function is not differentiable. At x=2 L.H.D. =−2e−x∣∣x=2=−2e2 R.H.D. =−2e2 Therefore, |f(x)| is not differentiable at x=0 and x=3 ∴ There are only 2 points where function is not differentiable.  Suggest Corrections  0      Similar questions  Related Videos   Graphical Interpretation of Differentiability
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