> # Solution to Maple 2 by the good doctor

> # exact, approx:=evalf(exact)

> exact:=(3/2)^100;approx:=evalf(exact);

exact := 515377520732011331036461129765621272702107...

approx := .4065611775e18

> # multiple graph plot

> plot([cos(x),1-x^2/2,1-x^2/2+x^4/4!,1-x^2/2+x^4/4!-x^6/6!],x=-2*Pi..2*Pi,y=-2..2,color=[black,gray,pink,red],thickness=[3,1,2,3],legend=["cos","degree 2", "degree 4", "degree 6"]);

[Maple Plot]

> # critical points

> f:=x^2*exp(-x);

f := x^2*exp(-x)

> f_prime:=diff(f,x);

f_prime := 2*x*exp(-x)-x^2*exp(-x)

> eqn:=f_prime=0;

eqn := 2*x*exp(-x)-x^2*exp(-x) = 0

> critical:=solve(eqn);

critical := 0, 2

> subs(x=0,f);subs(x=2,f);#Or

0

4*exp(-2)

> eval(f,x=0);eval(f,x=2);#Or

0

4*exp(-2)

> for i from 1 to 2 do subs(x=critical[i],f) od;

0

4*exp(-2)

> #equations

> restart;

> eqns:={p+q=S,p*q=P};

eqns := {p+q = S, p*q = P}

> S:=100;P:=900;solve(eqns);

S := 100

P := 900

{q = 10, p = 90}, {p = 10, q = 90}

> S:=50;P:=625;solve(eqns);

S := 50

P := 625

{p = 25, q = 25}, {p = 25, q = 25}

>