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The curve \( y(x)=a x^{3}+b x^{2}+c x+5 \) touches the \( x \)-axis at the point \( P(-2,0) \) and cuts the \( y \)-axis…

Q1

The curve \( y(x)=a x^{3}+b x^{2}+c x+5 \) touches the \( x \)-axis at the point \( P(-2,0) \) 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

[JEE Main 2022, 25 Jul (Shift 1)]

a

\( \frac{27}{4} \)

b

\( \frac{29}{4} \)

c

\( \frac{37}{4} \)

d

\( \frac{9}{2} \)

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