Concavity of y = x(cosx) at x = pi/3: Second Derivative Test

[donjt81]

I am doing this problem and I am getting stuck at solving the equation

problem: Use the second derivative test to determine the concavity of the following function. y = x(cosx) at x = pi/3

solution: y' = -xsinx + cosx
y'' = -xcosx - 2sinx = 0

and then i did
-xcosx = 2sinx ( i don't know if this is correct)
and then I am stuck... i don't know how to proceed.

please help

 

[Max Eilerson]

The function is upward concave is f''(x) > 0, and downward concave if f''(x) < 0. So just plug x=pi/3 into your function for y''.

 

[donjt81]

ohhhh! duhhh! I shouldve known... thanks