[填空题]
Sandy is on a holiday in Hawaii and takes a e5slddo idq39ww* 5n oi-/m, tparasailing ride on a beach. z4nhgzw)h lhc (p(, uu4f8o9tShe is towed behind a motor boat4,g(pu4 z8cfnh(hzu) ohtl 9w and attached to the parasail. The vertical height of the parasail over the first part of the ride can be modelled by the equation
$h(x)=\frac{2 x^{3}}{45}-\frac{17 x^{2}}{15}+8 x$
for $0 \leq x \leq 15$ , where $x \mathrm{~m}$ is the horizontal distance from the start, and $h \mathrm{~m} $ is the vertical height.
1. Find $h^{\prime}(x)$ =$\frac{a}{b}$$x^2$-$\frac{c}{b}$+d;a= ,b= ,c= ,d= .
2. Solve $h^{\prime}(x)$=0 x= or x= .
3. Using your answer to part (b), find the coordinates of the turning points of h(x) .
4. Sketch the graph of h(x) for $0 \leq x \leq 15$ , labelling the turning points.
5. If the parasail reaches a height level of $12 \mathrm{~m}$ , Sandy might suffer from vertigo. Find the x value for which this first happens.
6. When the gradient is negatively steeper than $-\frac{3}{2}$ , Sandy screams. Find the x value for which this first happens.
x= .
