InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
The points where the function `f(x) = [x] + |1 - x|, -1 < x < 3` where `[.]` denotes the greatest integer function is not differentiable, areA. `(-1,0,1,2,3)`B. `(-1,0,2)`C. `(0,1,2,3)`D. `(-1,0,1,2)` |
|
Answer» Correct Answer - C We have `f(x)={{:(,-x,-1 lexlt0),(,1-x,0lexlt1),(,x,1lexlt2),(,1+x,2lexlt3),(,5,x=3):}` Clearly, f(x) is discontinuous at x=0,1,2 and 3. So, it is not differentiable at these points. At x=-1, we have `underset(x to 1^(+))lim f(x)=underset(x to 1^(+))lim-x=1=f(-1)` So, it is continuous at x=-1 Also, (RHD at x=1)=-1 (a finite number). Therefore, f(x) is differentiable at x=-1 |
|