[填空题]
The cross-sectional view of a two-lane road tunne09 - qol0ercwwl system is0j+ on1n p:xqs shown on the axes below. The left and right lane tunnels are separated by a 2 metre thick concrete wall. The right-hand tunnel passes through the points 1q+ oxnj0:spn$\mathrm{A}$, $\mathrm{B}$, $\mathrm{C}$ and $\mathrm{D}$ and its height, in metres, above the base of the tunnel, is modelled by f(x)=-$0.04 x^{3}$+ 0.41 $x^{2}$, $4 \leq x \leq 10$ , relative to an origin $\mathrm{O} $.
Point A has coordinates (4,4) and point $\mathrm{D}$ has coordinates (10,1) .
1. Find the height of the right-hand tunnel when:
1. x=6 ; f(6)= (m)
2. x=8 ; f(8)= (m)
The left-hand tunnel can be modelled by a function g(x) , found by reflecting f(x) in the line x=3 .
2. Find the equation of g(x) .g(x)=$0.04 x^{3}-a x^{2}-bx+6.12$;a= ,b= .
3. 1. Find $g^{\prime}(x)$ .$g^{\prime}(x)=ax^{2}-b x-0.6$;a= ,b= .
2. Hence find the maximum height of the left-hand tunnel.
4. 1. Write down an integral which can be used to find the cross-sectional area of the left-hand tunnel.
2. Hence find the combined cross-sectional area of both tunnels.
