A curve has equation $y = (x - 3)\sqrt{x + 1} + 3$. These points lie on the curve. Any non-exact values are rounded to 4 decimal places. $A\,(2, k)$, $B\,(2.9, 2.8025)$, $C\,(2.99, 2.9800)$, $D\,(2.999, 2.9980)$, $E\,(3, 3)$.
(a)[1]
Find $k$, and give your answer correct to 4 decimal places.
(b)[1]
Find the gradient of $AE$, and give your answer correct to 4 decimal places.
(c)[2]
Rounded to 4 decimal places, the gradients of $BE$, $CE$ and $DE$ are $1.9748$, $1.9975$ and $1.9997$ respectively. State, with a reason, what these four gradient values indicate about the gradient of the curve at point $E$.
Worked solution & mark scheme
This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct value is $1.2679$.” …