(a)
Define continuity and differentiability of a function
at a point verify the continuity and differentiability
of the function :
(1 --X) x <1
f(x) = (1-x)(2-x) 1<x<2
(3-X)
x>2
Answers
Answered by
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Step-by-step explanation:
f(x)=∣x∣+∣x−1∣
It can be written as
f(x)=
⎩
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎧
−2x+1;
+1;
2x−1
x<0
0≤x<1
x≥1
At x=0
LHL=−2(0)+1=1
RHL=1
LHD=−2
RHD=0
Continuous but not differentiable on x=0
At x=1 LHL=2(1)−1=1
RHL=1
LHD=1
RHD=2
Continuous but not differentiable on x=1
Continuous everywhere in (−1,2) but not differentiable on x=0, 1 in (−1,2).
I hope it will helps you
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