# Question 2:

## Part (a)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x^n \rightarrow x^{n+1}$, i.e. $x^{1.5}$ or $x^2$ or $x$ seen (not for "$+ c$") | M1 | For $x^n \rightarrow x^{n+1}$ |
| Two out of three terms correct un-simplified or simplified (ignore $+c$) | A1 | |
| $2x^{1.5} - 3x^2 + 4x + c$ | A1 | All correct and simplified on one line including "$+ c$". Allow $\sqrt{x^3}$ for $x^{1.5}$ but not $x^1$ for $x$. |

**Ignore any spurious integral signs.**

## Part (b)(i)
*(Mark (b)(i) and (ii) together and must be differentiating the original function not their answer to part (a))*

| Answer/Working | Mark | Guidance |
|---|---|---|
| $x^n \rightarrow x^{n-1}$, i.e. $x^{0.5} \rightarrow x^{-0.5}$ or $6x \rightarrow 6$ | M1 | For $x^n \rightarrow x^{n-1}$ |
| $\frac{3}{2}x^{-0.5} - 6$ | A1 | For $\frac{3}{2}x^{-0.5} - 6$ or equivalent. May be un-simplified. Allow $\frac{\frac{3}{2}}{\sqrt{x}} - 6$ |

## Part (b)(ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{3}{2}x^{-0.5} - 6 = 0 \Rightarrow x^n = \ldots$ | M1 | Sets their $\frac{dy}{dx} = 0$ (may be implied by their working) and reaches $x^n = C$ (including $n=1$) **with correct processing allowing sign errors only**. May be implied by e.g. $\sqrt{x} = \frac{1}{4}$ or $\frac{1}{\sqrt{x}} = 4$ |
| $x = \frac{1}{16}$ cso | A1 | Allow equivalent fractions e.g. $\frac{9}{144}$ or $0.0625$. If other solutions are given (e.g. likely to be $x = 0$ or $x = -\frac{1}{16}$) then this mark should be withheld. |

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