# How do you find the critical numbers of #y= 2x-tanx#?

##### 1 Answer

Nov 5, 2016

#### Explanation:

Note that a critical number of a function

So, we first need to find the derivative of the function.

#y=2x-tanx#

#dy/dx=2-sec^2x#

So, critical values will occur when:

#0=2-sec^2x#

Or:

#sec^2x=2" "=>" "secx=+-sqrt2" "=>" "cosx=+-1/sqrt2=+-sqrt2/2#

Note that this occurs at

Furthermore, note that

#2-sec^2x=2-1/cos^2x#

This is undefined when

So, we have critical values at