(i)[2]
Find the $x$-value of $A$.
(ii)[3]
Find the expression for $f(x)$.
(iii)[4]
Find the $x$-values of $B$ and $C$.
(iv)[4]
Find, showing all necessary working, the area enclosed by the shaded region.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The diagram depicts the curve $y = f(x)$ for $x > 0$. It has a minimum at $A$ and meets the $x$-axis at $B$ and $C$. You are given that $\frac{dy}{dx} = 2x - \frac{2}{x^3}$ and that the curve goes through the point $\left(4, \frac{189}{16}\right)$.