Maximum Value of $g(x)=(8+x)^3(8-x)^4$ I think there can not be a maximum value of this, as if I plug $x=$1000, it will increase the value of the function in leaps and bounds. The answer says that the maximum value will occur at $x=-8/7$. What am I missing here?

You can use the wavy curve approach to find the range in which the local extremas and global extremas.
The wavy curve method is specifically used for polynomial equations.
Using this method you can easily come to know that there is no global maxima and global minima. However in the range (-8,8) there exists a local maxima. That point is x=-8/7
