You can check the answer you got by examining the properties of the first derivative. When the first derivative is zero, the function is either at a maximum or a minimum. Now, if we want a maximum, that means the function will be increasing up until that point, then decreasing afterwards. If the function is increasing over a given interval, what does that say about the first derivative over the same interval? And what does it mean when the function is decreasing? Use those properties and verify that the first derivative behaves as you'd expect it to around your x value of ~3.6