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]}