Find the 2nd derivative, set to 0 and solve for x.
Solve for x.
PH, I think you have a small typo in your derivative. Should be
. You have
The solution is, indeed, -1.89. I ran it through the ol' TI-92 to make doubly sure.
You may use the Intermediate Value Theorem. You can try x=-1.88 and get 0.055699
x=-1.9 and get -0.0232895.
Note the sign change. Therefore, you know it's between -1.88 and -1.9. Whittle away.