Is f(x)=-x^3+2x^2-2x-2f(x)=−x3+2x2−2x−2 concave or convex at x=1x=1?
1 Answer
May 24, 2016
concave at x = 1
Explanation:
To determine if f(x) is concave/convex at x = a , we consider 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+2x^2-2x-2f(x)=−x3+2x2−2x−2 differentiate using the
color(blue)"power rule"power rule
rArrf'(x)=-3x^2+4x-2 and
f''(x)=-6x+4
rArrf''(1)=-6+4=-2 Since f''(1) < 0 , then f(x) is concave at x = 1
graph{-x^3+2x^2-2x-2 [-10, 10, -5, 5]}
