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Year 12 Maths 2 Unit Hard Maths
Question

Consider the function whose derivative is given by

$\frac{dy}{dx}={\mathcal{x}}^{3}\left(\mathcal{x}-2\right)\left(\mathcal{x}+3\right)$. Which value of x will give a maximum turning
point on the graph of the function? Explain.

Find the exact volume if the region bounded by the curve y = 3log$\mathcal{x}$ ,
the x axis and x = 5, is rotated about the y axis.

Answer

• Maximum turning point at x=0

y=3log$\mathcal{x}$

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