Concavity Test: Finding the Concavity of y=2+3x-x^3 Using Derivatives

[phillyolly]

Homework Statement

y=2+3x-x³

The Attempt at a Solution

y'=3-3x²
y''=-6x

Please help me out finding the concavity of the function by using the Concavity Test or the Second derivative test.

 

[Raskolnikov]

y is concave down if y''< 0 and concave up if y''> 0. For what values of x is y'' negative? positive? The point at which y''= 0 is called an inflection. You should end up having y(x) as concave down for roughly half of its domain and concave up for the other half. You should be able to do the rest. And make sure to check whether the ends of the two sets of points are open or closed, i.e., do we need [a,b] or (a,b] or [a,b) or (a,b)?