# Is #f(x)=(x-1/x)# concave or convex at #x=-1#?

##### 1 Answer

Feb 10, 2017

Since

#### Explanation:

The convexity and concavity of a function can be determined through its second derivative. At

- convex (commonly known as concave up) if
#f''(a)>0# - concave (commonly known as concave down) if
#f''(a)<0#

Find the function's second derivative by rewriting with a negative power then using the power rule:

#f(x)=x-1/x#

#f(x)=x-x^-1#

#f'(x)=1-(-1x^-2)#

#f'(x)=1+x^-2#

#f''(x)=-2x^-3#

#f''(x)=-2/x^3#

The value of the second derivative at

#f''(-1)=-2/(-1)^3=-2/(-1)=2#

Since