Number of point where sgn(|sin x|)is non derivable but continuous in [0, 2π] is equal to
Answers
Answer:
ZERO
Step-by-step explanation:
This question is of the type that can be solved by graphs easily. One simply needs to know what the graph of |sin x| looks like.
In order to plot the graph of absolute value of any function first plot the graph of that function and then take a mirror image w.r.t. the x-axis that is to say that whatever lies beneath the x-axis will go up the x-axis.
The graph of |sin x| is attached.
From the graph we can say that the graph is continuous everywhere but is non-derivable wherever there is sharp change in value.
In the interval [0, 2π], there are 5 such points (at, -2π, -π, 0, π and 2π) where the function is non derivable.
Edit: I realised that the graph given is sgn(|sin x|) which is nothing but |sin x| /|sin x| =1
Thus the graph really is of f(x) = 1 which is a continuous and differentiable everywhere.
Thus the points where the funtion is non derivable is zero.
Hope the answer is helpful.
