# How do you find local maximum value of f using the first and second derivative tests: #f(x) = x / (x^2 + 9)#?

##### 1 Answer

The first derivative yields a critical point at

The second derivative

Since

#### Explanation:

**Given**:

**Required**: Local Maxima

**Solution Strategy**:

1) Take the 1st derivative to find the critical point,

2) Take the 2nd derivative and evaluate it at

- If
#(d^2f(x))/dx^2|_(x=c)>0; => "local minimum"# - else
#(d^2f(x))/dx^2|_(x=c)<0; => "local maximum"#

1) Use quotient rule to differentiate f(x)

Now set

2)