Is #f(x)=(x-1/x)# concave or convex at #x=1#?
1 Answer
Aug 19, 2017
Explanation:
#"to determine if a function is concave/convex at f(a)"#
#"we require to evaluate "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)=x-1/x=x-x^-1#
#rArrf'(x)=1+x^-2#
#rArrf''(x)=-2x^-3=-2/(x^3)#
#rArrf''(1)=-2<0#
#rArrf(x)" is concave at x = 1"#
graph{x-1/x [-10, 10, -5, 5]}