A curve has equation $y = 0.2x^5 + 3x^3 - 10x$. Find the $x$-coordinates of the stationary point

Question

A curve has equation $y = 0.2x^5 + 3x^3 - 10x$. Find the $x$-coordinates of the stationary points, $A$ and $B$, on the curve.[4] It is given that $P$ is a point on the curve where the gradient is a minimum. Show that $P$ and the midpoint of $AB$ are the same point.[4]

Accepted Answer

(i) $x=-1,\ 1$. (ii) $P=(0,0)$, which is the midpoint of $AB$.

2025 SST PRELIMS P1 Q9

2025 SST PRELIMS P1 Q9

Solution:

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