Sketch, for $x \ge 0$, the graphs of $y = x^2 - 6x + 5$ and \(y = 6 \left( 1 - \frac{1}{x}

Question

Sketch, for $x \ge 0$, the graphs of $y = x^2 - 6x + 5$ and $y = 6 \left( 1 - \frac{1}{x} \right)$ on the same diagram, stating the equations of any asymptotes and the coordinates of the points where $y = x^2 - 6x + 5$ and $y = 6 \left( 1 - \frac{1}{x} \right)$ intersect.[3] Show that the area of the region between the two graphs is $k - 6 \ln 6$, where $k$ is an exact constant to be found.[4]

Accepted Answer

(a) Positive intersections $(1,0)$ and $(6,5)$; asymptotes $x=0$, $y=6$. (b) $k=\dfrac{115}{3}$.

2024 VJC H1 Q5

2024 VJC H1 Q5

Solution:

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