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Question

If f(x) = |x| + |x - 1|, write the value of ddx (f(x)).

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Solution

f(x)=|x|+|x1|

when x>1

f(x)=x+x1=2x1

ddx(f(x))=2

when 0<x<1

f(x)=xx+1=1

ddx(f(x))=0

when x<0

f(x)=xx+1=2x+1

ddx(f(x))=2

ddx(f(x))=2, x>10, 0<x<12,x<0


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