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restart;
u:=x^2+3*x^7-sin(x);
f:=x->x^2+3*x^7-sin(x);
f(0);
f(1);
subs(x=0,u);
subs(x=1,u);
dudx:=diff(u,x);
D(f);
# Example 1 of mixing functions and expressions up.
D(u);
# Example 2 of doing it wrong.
diff(f,x);
diff(f(x),x);
solve(dudx=0,x);
plot(dudx,x=-1..1);
fsolve(dudx=0,x=0.5);
Digits:=60;
fsolve(dudx=0,x=0.5);
# Problem 4.5#8 in Ellis and Gullick handout
eq1:=(w/2)^2+h^2=r^2;
A:=h*w;
S1:=solve(eq1,w);
S1[1];
A2:=subs(w=S1[1],A);
dAdh:=diff(A2,h);
dAdh2:=simplify(dAdh);
A3:=solve(dAdh2=0,h);
# The answer to problem 4.5#8
A3[1];

restart;
# Problem 4.5#16 in Ellis and Gulick
eq2:=250=l*x*x;
C:=2*(2*p)*x^2+4*p*l*x;
S2:=solve(eq2,l);
C2:=subs(l=S2,C);
dCdx:=diff(C2,x);
S3:=solve(dCdx=0,x);
# Solution to 4.5#16
S3[1];


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