$N(p)$ boxes $of$ nails $atp$ dollars per box, $as$ given $by$ the following function. Complete parts $(a)$ through $(d).$

$N(p)=90-5p^2$;$(2p5)$

$(a)$ The average rate $of$ change $off(x)$ with respect $toxasx$ changes from $atob\underset{b0}{lim}\frac{f(a-b)+f(a)}{b}f(b)-f(a)\underset{b0}{lim}\frac{f(a+b)-f(a)}{b}\frac{f(b)-f(a)}{b-a}$$$3$$$4a$