JEE Math Practice 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:
- A.$$\frac{27}{4}$$
- B.$$\frac{29}{4}$$
- C.$$\frac{37}{4}$$
- D.$$\frac{9}{2}$$
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