I want to get solutions (approximate solutions) of the inequality g(x) > 0. I tried. 
 

restart; 
fprime := x-> (x-1)*(x-2)^2*(x-3)*(x-4); 
f := unapply(simplify(int(fprime(x), x)), x); 
g := unapply(expand(f(3*x+1)-x^3+3*x), x); 
solve(g(x) > 0, x);

I got

I have triangle TAD. Now I want to take any point inside the triagle TAD. How can I take it? I tried
 

restart; 
with(Student:-MultivariateCalculus); 
A := [1, 2, 3]; 
DD := [-2, 1, 0]; 
T := [1/2, 1/2, 3/2]; 
P := Plane(T, A, DD); 
GetRepresentation(P)

I got the quation of the plane TAD is
 

-3*x-3*y+4*z = 3

With the point P(x,y,z). What is the condition of x, y, z?

I have a picture. I tried to find the formula of the curve
My code

t := proc (x) options operator, arrow; b*x^10+c*x^9+d*x^8+e*x^7+f*x^6+g*x^5+h*x^4+i*x^3+j*x^2+k*x+l end proc

And solve
solve([t(-2) = 2, t(0) = -2, t(1) = 0, t(2.5) = -3, t(3.5) = 0, t(-1) = 0, eval(diff(t(x), x), x = -2) = 0, eval(diff(t(x), x), x = 0) = 0, eval(diff(t(x), x), x = 2.5) = 0, eval(diff(t(x), x), x = 1) = 0, t(2.8) = 0], [b, c, d, e, f, g, h, i, j, k, l])

[[b = -0.2688965311e-1, c = .1687428810, d = -0.3166922031e-1, e = -1.490599337, f = 1.885667707, g = 3.845330330, h = -6.939129440, i = -2.523473874, j = 7.112020606, k = 0., l = -2.]]

I ploted

plot(-.2688965311*x^10+.1687428810*x^9-.3166922031*x^8-1.490599337*x^7+1.885667707*x^6+3.845330330*x^5-6.939129440*x^4-2.523473874*x^3+7.112020606*x^2-2, x = -3.5 .. 4.5)

The result too far with picture. How can I repair?

I am trying to get the function of the curve in this picture. But, I don't know how to start. How can I get function of the graph in this picture?
I guess f(x) = (x + 1) (x - 1) (x - 3), if -1 <= x <=3.5 and f(x) = -(x + 1) (x + 2.5), if -2.5 <=x <=-1.

I am trying to  solve the system of equations
with(RealDomain);
solve(x^2+y^2+z^2-4*x+6*y-2*z-11 = 0, 2*x+2*y-z = -18], [x, y, z]);

I didn't get the result x = - 4/3, y = -19/3, z = 8/3.

How can I get the solution?

With Mathematica, I tried 
Solve[{x^2 + y^2 + z^2 - 4*x + 6*y - 2*z - 11 == 0, 
  2*x + 2*y - z == -18}, {x, y, z}, Reals]

And got the correct solution.