The equation of a curve is $$$y=54 x-(2 x-7)^{3}$$$. Find $$$\frac{\mathrm{d} y}{\mathrm{~d} x}$$$ and $$$\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_12 Year：2020 Question No：10(a)

Answer:

$\frac{\mathrm{d} y}{\mathrm{~d} x}=54-6(2 x-7)^{2}$
$\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=-24(2 x-7)$
(FT only for omission of ' $\times 2$ ' from the bracket)

Knowledge points:

1.7.2 use the derivative of (for any rational ), together with constant multiples, sums and differences of functions, and of composite functions using the chain rule

Answer:

Knowledge points:

Solution:

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