What are the critical points of #f(x) = 3x-arcsin(x)#?
1 Answer
Nov 1, 2015
Explanation:
To find critical points, simply derive and find zeroes of the derivative:
- The derivative of
#3x# is#3# ; - The derivative of
#arcsin(x)# is#1/sqrt(1-x^2)# ; - The derivative of a difference of functions is the difference of the derivatives of the functions.
Put these three things along and you have
Now we must find its zeroes:
(provided
We can easily solve this last equation:
And since