# 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]}