Question
Mathematics Question on Differentiability
The number of points, where the function f: R → R, f(x) = |x – 1|cos|x – 2|sin|x – 1| + (x – 3)|x2 – 5x + 4|, is NOT differentiable, is
A
1
B
2
C
3
D
4
Answer
2
Explanation
Solution
f :R->R.
f(x) = |x - 1| cos |x - 2| sin |x - 1| + (x - 3) |x2 - 5x + 4|
= |x - 1| cos |x - 2| sin |x - 1| + (x - 3) |x - 1||x - 4|
= |x - 1| [cos |x - 2| sin |x - 1| + (x - 3) |x - 4|]
Sharp edges at x = 1 and x = 4
∴ Non-differentiable at x = 1 and x = 4.