I have a question on a paper that I have to solve though I have become unsure as to what to do.
The problem is as follows
Given that y=16x+x^-1, find the two values of x for which dy/dx = 0.
When I differentiate I get 16 + x^-2 or 16 + 1/x^2 Mr F says: This is wrong. It should be 16 - x^-2 or 16 - 1/x^2.
to remove the fraction I multiply both sides by x^2 giving
16x^2 + 1 = 0
so dy/dx = 0 -> 16x^2 + 1 = 0.
I thought to obtain the two values of x you have to factorise the quadratic, and I am not sure how to do this given the form of the derived equation.
Any help with this would be gratefully appreciated.