Given $f(x)=x^2-x-lnx$

$(10$

a$)$ Find the intervals on which is increasing or decreasing.

b$)$ Find the local maximum and minimum values of $.$

c$)$ Find the intervals of concavity and the inflection points.

a$)$

$f^{\text{'}}(x)=2x-1-\frac{1}{x}=0$

$2x-1-\frac{1}{x}=0$

$(2x+1)(x-1)$

$x=-\frac{1}{2}orx=1$