For what values of the numbers and does the function have the maximum value

We've done the derivative tests.

Plug 2 in for x.

But if , then would be always zero.

Plug 2 in for x.

For the product to be less than zero (so the function is concave down giving a max), the factors have to have opposite signs.

But so

Back at the start:

Is that right? Thx.