How to find the points of of non-differentiability of a given function without graphs?
Given a function :
#f(x) = max{2 sinx, 1-cosx}, x in (0,pi) #
Find the points of non-differentiability.
I tried thinking analytically, and wrongly concluded that there are no points of non-differentiablilty as the function is defined at all point.
I would like to know:
- What is the correct approach to such questions?
- How to solve it intuitively, if possible?
Regards & Thanks
Aditya
Given a function :
Find the points of non-differentiability.
I tried thinking analytically, and wrongly concluded that there are no points of non-differentiablilty as the function is defined at all point.
I would like to know:
- What is the correct approach to such questions?
- How to solve it intuitively, if possible?
Regards & Thanks
Aditya
1 Answer
Please see below.
Explanation:
-
I assume that there are multiple correct approaches to such questions. (I'm not sure what you mean by a "correct approach", but I would call any approach that yields a correct answer to the question a correct approach.)
-
I don't know what you would count as an intuitive versus and non- (or un-) intuitive solution.
Here is how I would find an answer to the question:
Note that
The only place(s) that
Find the
Solve
#2sinx=1-cosx# to get
#x=0# or#x = cos^-1(-3/5)#
Check to see it the transition from one being maximum to the other is a "smooth" transition. (See if the derivatives are equal.)
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