# What is the minimum value of #g(x) = (x-1)/(x^2+4)?# on the interval #[-2,2]#?

##### 1 Answer

Minimum value is at

#### Explanation:

On a closed interval, the possible locations for a minimum will be:

- a local minimum inside the interval, or
- the endpoints of the interval.

We therefore compute and compare values for

First: what is

#g'(x)=((1)(x^2+4)-(x-1)(2x))/(x^2+4)^2#

#color(white)(g'(x))=(x^2+4-2x^2+2x)/(x^2+4)^2#

#color(white)(g'(x))=-(x^2-2x-4)/(x^2+4)^2#

This will equal zero when the numerator is zero. By the quadratic formula, we get

#x^2-2x-4=0" "=>" "x=1+-sqrt 5 approx {"-1.236", 3.236}#

Only one of these

Now, we compute:

**1.**

**2.**

**3.**

Comparing these three values of