Question

Determine an expression for f(x) in which:
f(x) is cubic,
f(x) ¡Ý 0 when x ¡Ü 2,
f(x) < 0 when x > 2, and
f(0) = 4

Answer 1

I assume you meant:

f(x) >= 0 when x <= 2,
f(x) < 0 when x > 2, and
f(0) = 4

We know that there is a root at x=2, so

f(x) = a(x-2)(bx^2+cx+d)
f(0) = a(-2)(d) = -2ad = 4

That's all we know. So, if we let a=1, d = -2 and

f(x) = (x-2)(bx^2+cx-2)

Unless you have some other info, b and c can be anything.

If I got the definition of f(x) wrong, fix it and follow the logic.