Question

Find a positive number x such that the sum of 25x and 1/x is as small as possible.

Answer 1

\[f(x)=25x+\frac{1}{x}\]
\[f'(x)=25-\frac{1}{x^2}\] set = 0 and solve for x to get the critical points

Answer 2

25-1/x^(2)=0

Answer 3

Continuing from above:

25 -1/x^(2) = 0

-1/x^(2) = -25

1/x^2 = 25

And, then ....