Absolute Minimum and Maximum Word Problem

[Zerobu]

Homework Statement

Find a number in the closed interval [1/2, 3/2] such that the sum of the number and its reciprocal is
(a)as small as possible
(b) as large as possible

I am given the answer in the back of the book
The answer to a is 1
The answer to be is 1/2

Homework Equations

Here is my equation

S= x + 1/x

dS/dx = 1-1/x^2

The Attempt at a Solution

I was wondering if i should set the derivative equal to zero and find the zeroes for the derivatives?

 

[Dick]

Absolutely, you should do that. That will give the locations of the local extrema. And don't forget to check the endpoints as well.