# Is #f(x)=1/(x-1)-2x# concave or convex at #x=0#?

##### 1 Answer

Apr 10, 2017

#### Explanation:

To determine if f(x) is concave/convex at f( a) we require to find the value of f''( a)

#• "If " f''(a)> 0" then f(x) is convex at x = a"#

#• "If " f''(a)<0" then f(x) is concave at x = a"#

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

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

#rArrf''(x)=2(x-1)^-3=2/(x-1)^3#

#rArrf''(0)=2/(-1)^3=-2#

#"Since " f''(0)<0" then f(x) is concave at x = 0"#

graph{(1/(x-1))-2x [-10, 10, -5, 5]}