2 \includegraphics[max width=\textwidth, alt={}, center]{63a316f6-1c18-4224-930f-0b58112c9f71-2_341_1043_466_552} The diagram shows the curve \(y = \mathrm { f } ( x )\). The curve has a maximum point at ( 0,5 ) and crosses the \(x\)-axis at \(( - 2,0 ) , ( 3,0 )\) and \(( 4,0 )\). Sketch the curve \(y ^ { 2 } = \mathrm { f } ( x )\), showing clearly the coordinates of any turning points and of any points where this curve crosses the axes.

| | |
|---|---|
| Parts with correct split of $u = \ln x, \frac{dv}{dx} = x^4$ | *M1 |
| $\frac{x^5}{5}\ln x - \int \frac{x^5}{5} \cdot \frac{1}{x} (dx)$ | A1 |
| $\frac{x^5}{5}\ln x - \frac{x^5}{25}$ | A1 |
| Correct method with the limits | dep*M1 |
| $\frac{4e^5}{25} + \frac{1}{25}$ | A1 |
| (Not "+c") | (Not '+c') |

2\\
\includegraphics[max width=\textwidth, alt={}, center]{63a316f6-1c18-4224-930f-0b58112c9f71-2_341_1043_466_552}

The diagram shows the curve $y = \mathrm { f } ( x )$. The curve has a maximum point at ( 0,5 ) and crosses the $x$-axis at $( - 2,0 ) , ( 3,0 )$ and $( 4,0 )$. Sketch the curve $y ^ { 2 } = \mathrm { f } ( x )$, showing clearly the coordinates of any turning points and of any points where this curve crosses the axes.

\hfill \mbox{\textit{OCR FP2 2008 Q2 [5]}}