Solving a system of equations

Task

Find a polynomial function of degree three featuring the saddle point (1, 1), as well as the point (2, 2).

1.		In the Input Bar, define the function `f(x):= a x^3 + b x^2 + c x + d`.
2.	`p`	According to the task, the function value at x=1 is 1. Enter `p: f(1) = 1`; and press the Enter key. Hints: The input ":" names your equation, while the semicolon “;” suppresses the output.
3.	`q`	We also know that the function value at x=2 is 2. Enter `q: f(2) = 2;`into the Input Bar.
4.	`r`	Since (1, 1) is a saddle point, the first derivative equals 0 at x=1. Enter `r: f'(1) = 0;`Hint: The derivative of f can be written as f'.
5.	`s`	We also know that the second derivative equals 0 at x=1. Enter `s:f''(1) = 0;`
6.		Select rows two through five with your pointer and apply the Solve tool.
		Hints: Press and hold the Ctrl-key while clicking onto the corresponding row numbers to select several rows at the same time. You can achieve the very same by using the Solve command instead: `Solve({p, q, r, s}, {a, b, c, d})`
7.	`Substitute`	Enter `Substitute($1, $6)` into the Input Bar and press the Enter key. Note: You just substituted the undefined variables in the formula of f (`$1`) with the solutions you just calculated (`$6`).
8.		Activate the disabled Visibility button below row number 7 to plot the function in the Graphics View.