I have a family of functions characterized by

f:=x^2+b*x+b*3;

I plotted some of them:

graph1:=x->subs(b=0,f):
graph2:=x->subs(b=2,f):
graph3:=x->subs(b=4,f):
plot([graph1(x),graph2(x),graph3(x)],x=-10..3,y=-5..15);

And now I want to draw a line through all maxima into the same diagram. The maxima have the coordinates (-1/2*b | -1/4*b^2+3*b). I managed to create a pointplot:

I need to calculate the following conditional expectation

with the marginal density

and

being the density function of a normal N(mu, sigma) distributed random variable

I want to differentiate the following (example) sum with respect to each variable.

foo:=sum(x[i]^2,i=1..3);

By hand I solved it like that:

g1:=diff(foo,x[1])=0;
g2:=diff(foo,x[2])=0;
g3:=diff(foo,x[3])=0;
solve({g1,g2,g3}, [x[1], x[2], x[3]]);

This works for i=1..3 but later I want to have it approach infinity. I don't have that much time to do it by hand -- what's a cleaner solution?

Hi,

I'm trying to simplify the following:

simplify((x^3)^(2/3));

I'm expecting x^2 but Maple doesn't simplify anything. Why not? I'm clueless.