(a)[2]
For $y = x^2 - 2x + \frac{12}{x}$, $x \ne 0$. Complete the values table.
(b)[5]
On the grid, sketch the graph of $y = x^2 - 2x + \frac{12}{x}$ for $-4 \le x \le -0.5$ and $0.5 \le x \le 4$.
(c)[3]
By drawing a suitable tangent, estimate the gradient of the graph at the point $(1,11)$.
(d)[3]
The equation $x^2 - 2x + \frac{12}{x} = k$ has exactly two distinct solutions. (i) Use the graph to find the value of $k$. (ii) Find the solutions of the equation.
(e)[3]
The equation $x^3 + ax^2 + bx + c = 0$ may be solved by plotting the line $y = 3x + 1$ on the grid. Find the values of $a$, $b$ and $c$.