(i)[3]
Determine the $x$-coordinate of $A$.
(ii)[6]
Given that the curve also passes through the point $(4, 10)$, determine the $y$-coordinate of $A$, and give your answer as a fraction.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The curve is defined by $y = f(x)$, and it is stated that $f'(x) = 3x^{\frac{1}{2}} - 2x^{-\frac{1}{2}}$. Point $A$ is the sole point on the curve where the gradient equals $-1$.