Short Answer of Differentiation and Its application

 Differentiation and Its Application (2014-2016)

1.   $2 x-6 x^{-2} \quad$
2.   $4+\frac{1}{2 x^2}$
3.   (a) $\frac{1}{2}+\frac{1}{2 x^2}$ (b) $x=\frac{1}{5}, 1$
4.   $6 x+9 x^{-4} \quad$
5.   (a) $\frac{x(2 x-5)}{3}$ (b) $x=\frac{5}{4}$
6.   (a)  $3 x^2+5 x-2$ (b) $x=\frac{1}{3}, x=-2$
7.   (a) $ 8 x+x^{-2} $ (b) $x=-\frac{1}{2} $
8.   (a) $4 y+x \quad$ (b) $x(4 y+x)$ (c) Show (d) 4.3 (e) $84,62.3, 57$ (f) curve (g) $ x \in[2.2,2.4]$
9.   (a) $1+\frac{4}{x^2}$ (b) $(0.5,-7.5)$
10.   $x=\frac{4}{10}, \frac{2}{5}$
11.   (a) $A=\frac{3}{2} \pi r^2+3 \pi r h \quad$ (b) $h=\frac{40}{\pi r^2} \quad$ (c) $A=\frac{3}{2} \pi r^2+\frac{120}{r}$ (d) $r=2.34 \mathrm{~cm} \quad$
12.   (a) $-3 x^2+10 x-8$ (b) $(1,0)$
13.   (a) $A=2x^2+4y$ (b) $y=\frac{36}{x^2}$ (c) show (d) $x=3.3$ (e) $80,66,78.8$ (f) Curve drawn.
14.   (a)show (b) minimum
15.   $ 18 t^2-30 t  \quad$
16.   (a) $6 t-4$ (b) $\frac{4}{6}$ (c) $23 $m 
17.   (a) $4 \quad$ (b) $t=2 \quad$ (c) $-12$
18.   (a) $90+28 t-3 t^2$ (b) $\sqrt{1864}, 11.9 \quad$
19.   (a) $t(2 t-5)(t-4)$ (b) $t=2.5,4$ (c) $12 t^2-52 t+40$ (d) $12 t^2-52 t+40=0, t=\frac{10}{3}, t=1$ (e) $20 \mathrm{~m} / \mathrm{s}^2$
20.   (a) $6t^2+14t+13$ (b) $12t+14$ (c) $t=0.274$
21.   (a) $125(\mathrm{~m})$(b) $t=5 \quad$ (c) $v=-20$ (accept 20)
22.   (a) $5 t^2-9 t-2$ (b) $t=2$
23.   (a) $v=18 t^2-4 t^3$ (b) $s=137 \quad $