Critical numbers and extrema and extreme values question

Question

A.) Find all critical numbers for the function f(x)= 2 sin x-x for 0 < x< pi

 

 

B.) Find the extrema and extreme values of f(x)= x/x^2+1

Answer 1

The technique for this is the same as for the other questions you've posted.

To find the critical points, take the derivative of the function, set it to zero, and solve for x.  The values of x that you get are the critical numbers as long as f(x) exists at those points. Try it out.