Mathematics 0580 · IGCSE · Differentiation

Differentiation — practice question

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.

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