Given that y = 16x + x^(-1), find the two values of x for which dy/dx = 0

The first thing required is to find out what dy/dx is in terms of x. For this, we need to differentiate y with respect to x which be can so to each term of the polynomial. All you need to do is mutiply the term (e.g. ax^b) by the the exponential, and lower the exponential by 1 (e.g. abx^(b-1). Hence:

dy/dx = 16 - x^(-2)=0

=> need x^(-2)=16

=> 1=16x^2

=> x=1/4 or x=-1/4