AM Applications of Differentiation Practice Question 1
The diagram shows part of the curve $y=x\left( \frac{k}{\sqrt{x}}-1 \right)$, where $A$ is a point on the curve and $k$ is a positive constant. Given also that $y=\frac{25}{4}$ is a tangent to the curve at $A$,
(i)
determine the value of $k$.
As $x$ gets large, the curve tends towards the line $l$.
(ii)
Explain why the gradient of $l$ is $-1$ and write down its equation.
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