Single variable optimization

[Lippi86]

Consider the function ln(x) + x/4 where 1 <_ x <_ 10

a) Find all stationary points for f(x)
b) Find all local extreme points and calculate local extreme values (ln (10) = (almost equal) 2.303)
c) Calculate the second derivative and determine if the function is concave or convex on its
domain. If not, where is it convex and where is it concave?

First i have to derivate

Then i get 1/x - 4x^-2 = 0

How do i go further now?

Thanks for the help

 

[galactus]

\(\displaystyle f(x)=ln(x)+\frac{x}{4}, \;\ 1\leq x\leq 10\)

\(\displaystyle f'(x)=\frac{1}{x}+\frac{1}{4}\)

\(\displaystyle f''(x)=\frac{-1}{x^{2}}\)

Here is the graph with the region shaded from 1 to 10.

concavity?.