A sketch of the graph of $y=f(x)$ for $-1.5 \le x \le 6$ is shown. Five labelled points on the graph of $y=f(x)$ are marked on the diagram: $A(-1.5,7.9)$, $B(-1,7)$, $C(1.2,10)$, $D(5,3)$ and $E(6,5.5)$.
(a(i))[1]
If $f(x)=k$ has two solutions in the interval $-1.5 \le x \le 6$, State one possible integer value of $k$.
(a(ii))[2]
If $f(x)=j$ has no solutions in the interval $-1.5 \le x \le 6$ whenever $j<a$ or $j>b$, find the greatest value of $a$ and the least value of $b$.
(b)[5]
State the coordinates of the two stationary points on the graph of $y = x^6 - 6x^5$. You must show all your working.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “4, 5, 7, 8, or 9” …