JEE Main 2014 · 11 Apr · Shift 1 · Mathematics Q71

MathematicsSingle correct+4 / -1Question 71 of 90

Let $f(x)=x|x|$ , $g(x)=\sin x$ and $h(x)=(g\circ f)(x)$ . Then

h(x)

is not differentiable at

x=0

h(x)

is differentiable at

x=0

, but

h'(x)

is not continuous at

x=0

h'(x)

is continuous at

x=0

but it is not differentiable at

x=0

h'(x)

is differentiable at

x=0

Answer and worked solution

Official answer: C

$h(x)=\sin(x|x|)$ and $h'(x)=2|x|\cos(x|x|)$ , which is continuous. But $2|x|$ has a corner at 0, so $h'$ is not differentiable there.

JEE Main 2014 · 11 Apr · Shift 1, Mathematics question 71