# For what values of x is #f(x)= x-cosx# concave or convex?

##### 1 Answer

Jan 16, 2016

#### Explanation:

Concavity is determined by the sign of the second derivative:

- If
#f''(a)>0# , then#f(x)# is convex at#x=a# . - If
#f''(a)<0# , then#f(x)# is concave at#x=a# .

First, determine the second derivative.

#f(x)=x-cosx#

#f'(x)=1+sinx#

#f''(x)=cosx#

So, we need to determine when

This occurs when

Thus,