Question

For what value of k will x+(k/x) have a relative maximum at x=-2?

Answer 1

f'(x) = d/dx x + kx^(-1)
f'(x) = 1 - kx^(-2)
f'(x) = 1 - k/x^2

Then, we can set this equal to zero to get:

1 - k/x^2 = 0
x^2-k = 0
Since x = -2:
(-2)^2 - k = 0
4 - k = 0
k = 4