For what values of x is f(x)= x-cosxf(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 , thenf(x) is convex atx=a . - If
f''(a)<0 , thenf(x) is concave atx=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,