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f(x) = maximum {4, 1+x^2, x^2 -1}, x belong R. total no of points where fx is non differentiable ? graphical approach if possible

f(x) = maximum {4, 1+x^2, x^2 -1}, x belong R.
total no of points where fx is non differentiable ?
 
graphical approach if possible

Grade:12th pass

2 Answers

Asish Mahapatra
36 Points
9 years ago
Hi Arpit,
 
First note that x^2 + 1 > x^2 – 1 for all x belonging to R
 
Therefore, max{4, x^2 -1, x^2+1} = max{4, x^2 + 1}
 
Now, x^2 + 1 is a quadratic expression and opens upwards. To find the region where x^2 + 1
 
x^2 + 1
=> x^2 – 3
=> (x + 3^0.5)(x – 3^0.5)
=> x lies between [ -sqrt(3), sqrt(3) ]
 
Thus, f(x) = 4,                      – sqrt(3)
                = x^2 + 1              elsewhere
 
Therefore the there are only two non-differentiable points (where the graph abruptly changes slope) which is at x = +/- sqrt(3)
Arpit Dhankar
33 Points
9 years ago
thank u for your help

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