h_1

f

h_0

a = 1 (slider from 0 to 4, step 0.05)
f(x) = ((a * x^(3)) * ((-1 / 8 * x) + 1 / 2)) + 2
max: f(2)
c_{1} = 1
g(x, k) = ((k * x^(3)) * ((-1 / 8 * x) + 1 / 2)) + 10
h1(x) = If[x ≥ 4, (-4 * (x - 4)) + 2]
gL: -1
gR: 6
gU: -2
gO: 8
f0(x) = If[0 ≤ x ≤ 4, f(x)]
f0c(x) = If[¬(0 ≤ x < 4), f(x)]
h0(x) = If[x ≤ 0, 2]
Text1: "f_{" + a + "}"