# Is #f(x)=-x^3+2x^2-2x-2# concave or convex at #x=1#?

##### 1 Answer

May 24, 2016

#### Answer:

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-2# differentiate using the

#color(blue)"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]}