generate a continuous and differentiable function f(x)

Question

what is the formula to generate a continuous and differentiable function f(x) with the following properties: f(x) is decreasing at x=−6 f(x) has a local minimum at x=−2 f(x) has a local maximum at x=2

Answer 1

-1*(x-2)^2*x*(x+2)^2

This function is constructed so that x =0 at -2,0, and 2, and x is positive on (-∞, -2) ∪ (-2, 0) and negative on (0, 2) and (2, ∞), so we have a minimum at -2 and a maximum at 2, and the function is monotone decreasing on (-∞, -2), which includes -6.