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,