Finding where function is concave upward

[Arkan]

Of this function:

f(x) = x^2(1-x)

This is my work:

Determining second dericative:
y = x^2-x^3

y' = 2x - 3x^2
y'' = 2-6x


Determining concavity:

2-6x>0
-6x>-2
x<1/3


But when I look at the graph it looks like the answer should be x<2/3

 

[Ishuda]

Of this function:

f(x) = x^2(1-x)

This is my work:

Determining second dericative:
y = x^2-x^3

y' = 2x - 3x^2
y'' = 2-6x


Determining concavity:

2-6x>0
-6x>-2
x<1/3


But when I look at the graph it looks like the answer should be x<2/3

The answer x\(\displaystyle \le\)1/3 is correct for the graph being concave. A local maximum occurs at x=2/3 (and a local minimum at x=0)

 

[lookagain]

The answer x\(\displaystyle \le\)1/3 is correct for the graph being concave [up].

The answer is x < 1/3.