Let f(x)=x3+3x2−9x+21\displaystyle {f{{\left({x}\right)}}}={x}^{{3}}+{3}{x}^{{2}}-{9}{x}+{21}.

(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\displaystyle {f} "(x)=\displaystyle {\left({x}\right)}=  

(c)   On what interval is f\displaystyle {f} increasing (do not include the endpoints in the interval)?
interval of increasing =  

(d)   On what interval is f\displaystyle {f} decreasing (do not include the endpoints in the interval)?
interval of decreasing =  

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

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

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