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IB MAI HL Calculus Topic 5.1 Differentiation (id: af3b9d6b5)

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admin 发表于 2024-2-25 23:21:58 | 显示全部楼层 |阅读模式
本题目来源于试卷: IB MAI HL Calculus Topic 5.1 Differentiation,类别为 IB数学

[填空题]
Sandy is on a holidayc vkc0l xogq 4gp09-).sc,bht 9znkd hf1u gd30bg56j in Hawaii and takes a parasailing ride on a beach. She is towed behind a motor boat and attached to the parasail. The vertical height of the parasail over the first pdj03hg g bz1u9kfdn65art 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=  .




参考答案:
空格1: 2空格2: 15空格3: 34空格4: 8空格5: 5空格6: 12空格7: 7.5


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