Is #f(x)=x^3-x^2+x-4# concave or convex at #x=-1#?
1 Answer
Feb 22, 2017
Explanation:
To determine if a function 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)=x^3-x^2+x-4#
#rArrf'(x)=3x^2-2x+1#
#rArrf''(x)=6x-2#
#"and "f''(-1)=-6-2=-8<0#
#rArrf(x)" is concave at "x=-1#
graph{x^3-x^2+x-4 [-10, 10, -5, 5]}
