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

##### 2 Answers

There is no such

#### Explanation:

Let

the

In order for

However,

There is a relative minimum when

#### Explanation:

Let

#f(x) = x+k/x#

Then differentiating wrt

# f'(x) = 1 - k/x^2 #

And differentiating again wrt

# f''(x) = (2k)/x^3 #

the

At a maximum or minimum we require

# f'(2)=0 => 1 - k/2^2=0#

# :. 1-k/4 = 0#

# :. k = 4#

So When

Now let's find the nature of this critical point. With

# f''(2) = ((2)(4))/2^3 > 0 # , Hence this a relative minimum