The equation of a curve is $$\(y=(3-2 x)^{3}+24 x\)$$. Find expressions for $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}\)$$ and $$\(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_11 Year：2020 Question No：9(a)
Answer:
\(\frac{\mathrm{d} y}{\mathrm{~d} x}=3(3-2 x)^{2} \times-2+24=-6(3-2 x)^{2}+24\)
\((\) B1 without \(\times-2\). B1 for \(\times-2)\)
\(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=-12(3-2 x) \times-2=24(3-2 x)\)
\(\left(\right.\) B1FT from \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) without \(\left.-2\right)\)
\((\) B1 without \(\times-2\). B1 for \(\times-2)\)
\(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=-12(3-2 x) \times-2=24(3-2 x)\)
\(\left(\right.\) B1FT from \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) without \(\left.-2\right)\)
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
Solution:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download