Let f(x)=x4−18x210\displaystyle {f{{\left({x}\right)}}}=\frac{{{x}^{{4}}-{18}{x}^{{2}}}}{{10}}.

(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 (include the endpoints in the interval)?
interval of increasing =  

(d)   On what interval is f\displaystyle {f} decreasing (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 concave downward =  

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

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