Let f(x)={max{|x|,x2},|x|≤28−2|x|,2<|x|≤4 Let S be the set of points in the interval (−4,4) at which f is not differentiable. Then S :
A
is an empty set
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
equals {−2,−1,1,2}
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
equals {−2,−1,0,1,2}
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
equals {−2,2}
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is C equals {−2,−1,0,1,2} For |x|≤2 f(x)=⎧⎨⎩x2,−2≤x≤−1|x|,−1<x<1x2,1≤x≤2 Therefore , For x∈[−4,4] f(x)=⎧⎪
⎪
⎪
⎪
⎪⎨⎪
⎪
⎪
⎪
⎪⎩8+2x,−4≤x<−2x2,−2≤x≤−1|x|,−1<x<1x2,1≤x≤28−2x,2<x≤4
f is not differentiable at x∈{−2,−1,0,1,2} ∴S={−2,−1,0,1,2}