Let f(x)=x3+6x215x+17\displaystyle {f{{\left({x}\right)}}}={x}^{{3}}+{6}{x}^{{2}}-{15}{x}+{17}.

(a)   Use the definition of a derivative or the derivative rules to find
f(x)=\displaystyle {f}'{\left({x}\right)}=  

(b)   Use the definition of a derivative or the derivative rules to find
f(x)=\displaystyle {f}{''}{\left({x}\right)}=  

(c)   On what interval is f\displaystyle {f} increasing?
interval of increasing =  

(d)   On what interval is f\displaystyle {f} decreasing?
interval of decreasing =  

(e)   On what interval is f\displaystyle {f} concave downward?
interval of downward concavity =  

(f)   On what interval is f\displaystyle {f} concave upward?
interval of upward concavity =