Easy -1.3 This is a straightforward application of the power rule for differentiation, applied twice. The only additional requirement is substituting x=36 and simplifying without a calculator, which involves basic arithmetic with powers (36^{-1/2} = 1/6). This is simpler than average A-level questions as it requires only routine differentiation and basic algebraic manipulation with no problem-solving or conceptual challenges.
10 Given tha \(y = 6 x ^ { \frac { 3 } { 2 } }\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
Show, without using a calculator, that when \(x = 36\) the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) is \(\frac { 3 } { 4 }\).
\(y' = 6 \times \frac{3}{2}x^{\frac{1}{2}}\) or \(9x^{\frac{1}{2}}\) o.e.
2
1 if one error in coeff or power, or extra term
\(y'' = \frac{9}{2}x^{-\frac{1}{2}}\) o.e.
1
f.t. their \(y'\) only if fractional power
\(\sqrt{36} = 6\) used; interim step to obtain \(\frac{3}{4}\)
M1 A1
f.t. their \(y''\); www answer given
## Question 10:
$y' = 6 \times \frac{3}{2}x^{\frac{1}{2}}$ or $9x^{\frac{1}{2}}$ o.e. | 2 | 1 if one error in coeff or power, or extra term
$y'' = \frac{9}{2}x^{-\frac{1}{2}}$ o.e. | 1 | f.t. their $y'$ only if fractional power
$\sqrt{36} = 6$ used; interim step to obtain $\frac{3}{4}$ | M1 A1 | f.t. their $y''$; www answer given | 5
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10 Given tha $y = 6 x ^ { \frac { 3 } { 2 } }$, find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ and $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$.\\
Show, without using a calculator, that when $x = 36$ the value of $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$ is $\frac { 3 } { 4 }$.
\hfill \mbox{\textit{OCR MEI C2 Q10 [5]}}