Higher November 2023 Paper 5 Q13

(a) Complete the table for \(y = x^3 + 4x^2\).

\(x\)	−5	−4.5	−4	−3	−2	−1	0	1
\(y\)	−25	−10.1	0	9	8		0	5

[1]

(b) Draw the graph of \(y = x^3 + 4x^2\) for \(-5 \leqslant x \leqslant 1\).

[3]

(c) The equation \(x^3 + 4x^2 = k\), where \(k\) is an integer, has exactly one solution for \(-5 \leqslant x \leqslant 1\).

Find the greatest possible value of \(k\). [1]