Question

# If f(x)=âŽ§âŽª âŽª âŽªâŽ¨âŽª âŽª âŽªâŽ©x2+2,x<0âˆ’2eâˆ’x,0â‰¤x<2,âˆ’2e2(xâˆ’3),xâ‰¥2 then

A
|f(x)| is discontinuous at 0 points
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
|f(x)| is discontinuous at 2 points
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C
|f(x)| is not differentiable at 2 points
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
|f(x)| is not differentiable at 3 points
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is C |f(x)| is not differentiable at 2 pointsGraph of f(x) Graph of |f(x)| The graph is discontinuous at 0 points Before x=0 the function is differentiable at all points because our function is a quadratic function. At x=2 and x=0, the function changes definition. So we need to check differentiability. At x=3, a linear function changes direction (sharp turn). So the function is not differentiable. At x=0 L.H.D. =0 R.H.D =−2e−x∣∣x=0=−2 So, function is not differentiable. At x=2 L.H.D. =−2e−x∣∣x=2=−2e2 R.H.D. =−2e2 Therefore, |f(x)| is not differentiable at x=0 and x=3 ∴ There are only 2 points where function is not differentiable.

Suggest Corrections
0
Related Videos
Graphical Interpretation of Differentiability
MATHEMATICS
Watch in App