2. After verifying that it is not possible to achieve what is required using a second-degree polynomial function, determine the coefficients $a, b, c, d \in \mathbb{R}$ of the function $f(x)$ polynomial of third degree that satisfies the stated conditions. Finally, represent the resulting tile in a Cartesian plane. Two different types of design are proposed to a customer, derived respectively from the functions $a_n(x) = 1 - x^n$ and $b_n(x) = (1-x)^n$, considered for $x \in [0,1]$, with $n$ a positive integer.
2. After verifying that it is not possible to achieve what is required using a second-degree polynomial function, determine the coefficients $a, b, c, d \in \mathbb{R}$ of the function $f(x)$ polynomial of third degree that satisfies the stated conditions. Finally, represent the resulting tile in a Cartesian plane.
Two different types of design are proposed to a customer, derived respectively from the functions $a_n(x) = 1 - x^n$ and $b_n(x) = (1-x)^n$, considered for $x \in [0,1]$, with $n$ a positive integer.