Question

Discuss the continuity and differentially f
unction f(x)=|x|+|x-1| in the interval(-1,2)

​

Answer 1

Answer:

ANSWER

f(x)=∣x∣+∣x−1∣

It can be written as

$f(x)= </p><p>⎩</p><p>⎪</p><p>⎪</p><p>⎪</p><p>⎨</p><p>⎪</p><p>⎪</p><p>⎪</p><p>⎧</p><p> </p><p> </p><p>−2x+1;</p><p>+1;</p><p>2x−1</p><p> </p><p> </p><p>x<0</p><p>0≤x<1</p><p>x≥1$

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).