a = 1 (slider from -5 to 5, step 0.1)
b = 2 (slider from -5 to 5, step 0.1)
c = 0 (slider from -5 to 5, step 0.1)
d = 0 (slider from -5 to 5, step 0.1)
e = 0 (slider from -5 to 5, step 0.1)
f(x) = (a * x^(3)) + (b * x^(2)) + (c * x) + d + e / x
f_1(x) = ((3 * a) * x^(2)) + ((2 * b) * x) + c - e / x^(2)
fa = If(a ≠ 0, If[a ≟ -1, "-x^3", If[a ≟ 1, "x^3", a + "x^3"]], "")
fb = If(b ≠ 0, If[(b > 0) ∧ (a ≠ 0), "+", ""] + (If[b ≟ 1, "x^2", If[b ≟ -1, "-x^2", b + "x^2"]]), "")
fc = If(c ≠ 0, If[(c > 0) ∧ (b ≠ 0), "+", ""] + (If[c ≟ 1, "x", If[c ≟ -1, "-x", c + "x"]]), "")
fb_2 = If(d ≠ 0, d, "")
fc_1 = If(d ≠ 0, d, "")
fd = If(d ≠ 0, If[(d > 0) ∧ (c ≠ 0), "+", ""] + d, "")
fe = If(e ≠ 0, If[e  <  0, "-", If[d ≠ 0, "+", ""]] + "\frac{" + abs(e) + "}{x}", If[a ≟ 0 ∧ b ≟ 0 ∧ c ≟ 0 ∧ d ≟ 0 ∧ e ≟ 0, "0", ""])
texte1: "f(x)=" + (LaTeX[fa]) + "" + LaTeX[fb] + "" + LaTeX[fc] + "" + LaTeX[fd] + "" + LaTeX[fe] + ""
f_1a = If(a ≠ 0, If[(3 * a) ≟ 1, "x^2", If[(3 * a) ≟ -1, "-x^2", (3 * a) + "x^2"]], "")
f_1b = If(b ≠ 0, If[(b > 0) ∧ (a ≠ 0), "+", ""] + (If[(2 * b) ≟ 1, "x", If[(2 * b) ≟ -1, "-x", (2 * b) + "x"]]), "")
f_1c = If(c ≠ 0, If[(c > 0) ∧ (b ≠ 0), "+", ""] + c, "")
f_1e = If(e ≠ 0, If[e > 0, "-", If[c ≠ 0, "+", ""]] + "\frac{" + abs(e) + "}{x^2}", If[a ≟ 0 ∧ b ≟ 0 ∧ c ≟ 0 ∧ e ≟ 0, "0", ""])
texte1_1: "f'(x)=" + (LaTeX[f_1a]) + "" + LaTeX[f_1b] + "" + LaTeX[f_1c] + "" + LaTeX[f_1e] + ""
r_1, r_2, r_3, r_4 = Root(((3 * a) * x^(4)) + ((2 * b) * x^(3)) + (c * x^(2)) - e)
p_1(x) = x  <  x(r_1)
p_2(x) = (x > x(r_1)) ∧ (x  <  x(r_2))
p_3(x) = (x > x(r_2)) ∧ (x  <  x(r_3))
p_4(x) = (x > x(r_3)) ∧ (x  <  x(r_4))
p_5(x) = x > x(r_4)
d_1: x = x(r_1)
d_2: x = x(r_2)
d_3: x = x(r_3)
d_4: x = x(r_4)