OCR MEI C2 — Question 12 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTangents, normals and gradients
TypeFind second derivative
DifficultyEasy -1.2 This is a straightforward differentiation exercise requiring only direct application of the power rule twice. The square root needs to be rewritten as x^(1/2), but this is standard C2 technique with no problem-solving or conceptual challenge beyond routine calculus mechanics.
Spec1.07d Second derivatives: d^2y/dx^2 notation1.07i Differentiate x^n: for rational n and sums
12 Given tha \(y = 6 x ^ { 3 } + \sqrt { x } + 3\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
Question 12:
AnswerMarks Guidance
\(\sqrt{x} = x^{\frac{1}{2}}\) soiB1
\(18x^2,\ \frac{1}{2}x^{-\frac{1}{2}}\)B1B1 \(-1\) if \(\text{d/d}x(3) \neq 0\)
\(36x\)B1
\(Ax^{-\frac{3}{2}}\) (from \(Bx^{-\frac{1}{2}}\))B1 any \(A, B\) 
## Question 12:

$\sqrt{x} = x^{\frac{1}{2}}$ soi | B1 |
$18x^2,\ \frac{1}{2}x^{-\frac{1}{2}}$ | B1B1 | $-1$ if $\text{d/d}x(3) \neq 0$
$36x$ | B1 |
$Ax^{-\frac{3}{2}}$ (from $Bx^{-\frac{1}{2}}$) | B1 | any $A, B$ | 5
12 Given tha $y = 6 x ^ { 3 } + \sqrt { x } + 3$, find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ and $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$.

\hfill \mbox{\textit{OCR MEI C2  Q12 [5]}}
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