# 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