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Question

The curve $y(x)=a x^{3}+b x^{2}+c x+5$ touches the $x$-axis at the point $\mathrm{P}(-2,0)$ and cuts the $y$-axis at the point $Q$, where $y^{\prime}$ is equal to 3 . Then the local maximum value of $y(x)$ is:

$\frac{27}{4}$
$\frac{29}{4}$
$\frac{37}{4}$
$\frac{9}{2}$

Solution

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