Econ 407, sept. 20, 1999, lecture notes and more examples of a application of derivatives.

> TR:=75*Q-4*Q^2;

> plot(75*Q-4*Q^2,Q=0..20);

> mr:=diff(75*Q-4*Q^2,Q);

> plot({TR,mr},Q=0..20);

> TC:=Q^2+7*Q+23;

> plot({TR,TC},Q=0..20);

> PR:=TR-TC;

> plot(PR,Q=0..20);

> DPR:=diff(PR,Q);

> solve(DPR,Q);

> MC:=diff(TC,Q);

> solve(MC=mr,Q);

>

> R:=4000*Q-33*Q^2;

> C:=2*Q^3-3*Q^2+400*Q+5000;

> P:=R-C;

> DP:=diff(3600*Q-30*Q^2-2*Q^3-5000,Q);

> solve(DP=0,Q);

> plot({R,C},Q=0..50);

> plot({R,C},Q=-50..50);

> Qd:=1400-p^2;

> plot(Qd,p=0..50);

> dQp:=diff(Qd,p);

> eval(Qd,p=20);

> el:=-2*20*20/1000.0;

>